diff --git a/BUILD b/BUILD index 0fcaf9f..368e645 100644 --- a/BUILD +++ b/BUILD @@ -134,8 +134,10 @@ cc_binary( cc_test ( name = "unit_test", copts = ["-std=c++14", "-Werror"], + includes = ["third_party/half"], srcs = [ "src/tim/vx/test_utils.h", + "third_party/half/half.hpp" ] + glob(["src/tim/**/*_test.cc"]), deps = [ "@gtest//:gtest", diff --git a/CMakeLists.txt b/CMakeLists.txt index 72691e6..f77c8c4 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -98,6 +98,8 @@ if(TIM_VX_ENABLE_TEST) FetchContent_Populate(googletest) add_subdirectory(${googletest_SOURCE_DIR} ${googletest_BINARY_DIR}) endif() + + include_directories(third_party/half) endif() if(TIM_VX_ENABLE_GRPC) diff --git a/include/tim/vx/ops/conv2d.h b/include/tim/vx/ops/conv2d.h index f609960..72b2265 100644 --- a/include/tim/vx/ops/conv2d.h +++ b/include/tim/vx/ops/conv2d.h @@ -99,12 +99,9 @@ class Conv2d : public BuiltinOp { const int32_t multiplier_; const DataLayout kernel_layout_; -#if defined(__clang__) && (__clang_major__ >= 15) -#define TIM_VX_OPS_CONV2D_WITH_F16BIAS 1 private: void OnBindInputPostProc(const std::shared_ptr& tensor, int32_t input_idx) override; -#endif }; } // namespace ops diff --git a/src/tim/vx/ops/conv2d.cc b/src/tim/vx/ops/conv2d.cc index 4f93b1c..d5130db 100644 --- a/src/tim/vx/ops/conv2d.cc +++ b/src/tim/vx/ops/conv2d.cc @@ -42,8 +42,8 @@ Conv2d::Conv2d(Graph* graph, const std::array pad, const std::array& stride, const std::array& dilation, int32_t multiplier, DataLayout input_layout, DataLayout kernel_layout) - : Conv2d(graph, 0, PadType::AUTO, {0, 0}, stride, dilation, pad, - multiplier, input_layout, kernel_layout) {} + : Conv2d(graph, 0, PadType::AUTO, {0, 0}, stride, dilation, pad, multiplier, + input_layout, kernel_layout) {} Conv2d::Conv2d(Graph* graph, int32_t weights, PadType padding, const std::array& ksize, @@ -88,41 +88,33 @@ std::shared_ptr Conv2d::Clone(std::shared_ptr& graph) const { this->kernel_layout_); } -const std::vector> Conv2d::ConstantInputsTensor() const { - if (this->IsAllInputsConst()) { +const std::vector> Conv2d::ConstantInputsTensor() + const { + if (this->IsAllInputsConst()) { return {this->impl_->inputs_tensor_[0]}; } else { return {}; } } -// Handle float16 bias if clang compiler is no less than 15.0.0 version -#ifdef TIM_VX_OPS_CONV2D_WITH_F16BIAS +// Handle float16 bias void Conv2d::OnBindInputPostProc(const std::shared_ptr& tensor, int32_t input_idx) { if (tensor->GetDataType() == vx::DataType::FLOAT16 && tensor->IsConstTensor() && impl_->inputs_tensor_.size() == 3) { - uint32_t bias_size = 1; - for (auto i : tensor->GetShape()) { - bias_size *= i; - } - std::vector<_Float16> in(bias_size); - tensor->CopyDataFromTensor(in.data()); + float* float32_bias = tensor->ConvertTensorToFloat32Data(); - std::vector out(bias_size); - for (uint i = 0; i < bias_size; i++) { - out[i] = static_cast(in[i]); - } TensorSpec fp32bias_spec(tim::vx::DataType::FLOAT32, tensor->GetShape(), tim::vx::TensorAttribute::CONSTANT); - auto out_tensor = impl_->graph_->CreateTensor(fp32bias_spec, out.data()); + + auto out_tensor = impl_->graph_->CreateTensor(fp32bias_spec, float32_bias); + vsi_nn_Free(float32_bias); impl_->inputs_tensor_[2] = out_tensor; impl_->node()->input.tensors[input_idx] = out_tensor->GetId(); impl_->graph_->RenewTensorConsumersMap(tensor, out_tensor, this); } } -#endif } // namespace ops } // namespace vx diff --git a/src/tim/vx/ops/conv2d_test.cc b/src/tim/vx/ops/conv2d_test.cc index 77db127..5332cf0 100644 --- a/src/tim/vx/ops/conv2d_test.cc +++ b/src/tim/vx/ops/conv2d_test.cc @@ -28,11 +28,12 @@ #include "tim/vx/context.h" #include "tim/vx/graph.h" #include "tim/vx/types.h" +#include "third_party/half/half.hpp" -#ifdef TIM_VX_OPS_CONV2D_WITH_F16BIAS TEST(Conv2d, shape_4_2_1_1_float16_PaddingTest) { auto ctx = tim::vx::Context::Create(); auto graph = ctx->CreateGraph(); + using namespace half_float::literal; tim::vx::ShapeType input_shape({4, 2, 1, 1}); //whcn tim::vx::ShapeType weight_shape({2, 2, 1, 3}); //whio @@ -50,26 +51,29 @@ TEST(Conv2d, shape_4_2_1_1_float16_PaddingTest) { tim::vx::TensorAttribute::OUTPUT); // Input data nchw - std::vector<_Float16> input_data = { - 1, 1, 1, 1, // row = 1 - 2, 2, 3, 2 // row = 2 + + std::vector input_data = { + 1.0_h, 1.0_h, 1.0_h, 1.0_h, // row = 1 + 2.0_h, 2.0_h, 3.0_h, 2.0_h // row = 2 }; // weight data oihw - std::vector<_Float16> weight_data = { - 1, 2, 3, 4, //first 2x2 filter - -1, 1, -1, 1, // second 2x2 filter - -1, -1, 1, 1, // third 2x2 filter + std::vector weight_data = { + 1.0_h, 2.0_h, 3.0_h, 4.0_h, //first 2x2 filter + -1.0_h, 1.0_h, -1.0_h, 1.0_h, // second 2x2 filter + -1.0_h, -1.0_h, 1.0_h, 1.0_h, // third 2x2 filter }; // bias data - std::vector<_Float16> bias_data = {1, 2, 3}; + std::vector bias_data = {1.0_h, 2.0_h, 3.0_h}; - // nchw - std::vector<_Float16> golden = {// first channel - 18, 22, 21, 8, 7, 9, 8, 3, 2, 3, 1, -1, - // second channel - 2, 3, 1, 0, 5, 6, 6, 4, -1, -2, -2, 1}; + std::vector golden = { + // first channel + 18.0_h, 22.0_h, 21.0_h, 8.0_h, 7.0_h, 9.0_h, 8.0_h, 3.0_h, 2.0_h, 3.0_h, + 1.0_h, -1.0_h, + // second channel + 2.0_h, 3.0_h, 1.0_h, 0.0_h, 5.0_h, 6.0_h, 6.0_h, 4.0_h, -1.0_h, -2.0_h, + -2.0_h, 1.0_h}; auto input_tensor = graph->CreateTensor(input_spec); auto weight_tensor = graph->CreateTensor(weight_spec, weight_data.data()); @@ -80,8 +84,8 @@ TEST(Conv2d, shape_4_2_1_1_float16_PaddingTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -98,11 +102,10 @@ TEST(Conv2d, shape_4_2_1_1_float16_PaddingTest) { for (auto i : output_tensor->GetShape()) { output_size *= i; } - std::vector<_Float16> output(output_size); + std::vector output(output_size); EXPECT_TRUE(output_tensor->CopyDataFromTensor(output.data())); - EXPECT_TRUE(ArraysMatch(golden, output, (_Float16)0.1)); + EXPECT_TRUE(ArraysMatch(golden, output, (half_float::half)0.1)); } -#endif TEST(Conv2d, shape_4_2_1_1_float32_PaddingTest) { auto ctx = tim::vx::Context::Create(); @@ -155,8 +158,8 @@ TEST(Conv2d, shape_4_2_1_1_float32_PaddingTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -224,8 +227,8 @@ TEST(Conv2d, shape_4_2_2_2_float32_PointwiseTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -295,8 +298,8 @@ TEST(Conv2d, shape_4_2_1_2_float32_SimpleTest) { std::array stride({2, 2}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -361,8 +364,8 @@ TEST(Conv2d, shape_4_2_2_2_float32_SimpleChannelsTest) { std::array stride({2, 2}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -432,8 +435,8 @@ TEST(Conv2d, shape_6_3_1_1_float32_SimpleAnisotropicStridesTest) { std::array stride({3, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -497,8 +500,8 @@ TEST(Conv2d, shape_4_3_1_1_float32_HandCalculatedTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -562,8 +565,8 @@ TEST(Conv2d, shape_4_3_1_1_float32_HandCalculatedConstFilterTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -627,8 +630,8 @@ TEST(Conv2d, shape_4_3_1_1_float32_HandCalculatedBiasTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -691,8 +694,8 @@ TEST(Conv2d, shape_4_3_1_1_float32_HandCalculatedValidTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -759,8 +762,8 @@ TEST(Conv2d, DISABLED_shape_4_2_2_2_float32_DisabledPointwiseMultifilterTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -827,8 +830,8 @@ TEST(Conv2d, shape_9_9_1_1_float32_SimpleDilationTest) { std::array stride({1, 1}); std::array dilation({3, 3}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -893,8 +896,8 @@ TEST(Conv2d, shape_4_2_1_2_float32_StrideTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -958,8 +961,8 @@ TEST(Conv2d, shape_4_2_1_2_float32_InputAndFilterSameWidthHeightTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -1011,13 +1014,13 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest1) { std::vector zero_point_output = {scales_zp.second}; tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2, - scales_input, zero_point_input); + scales_input, zero_point_input); tim::vx::Quantization quant_weight(tim::vx::QuantType::ASYMMETRIC, 2, - scales_weight, zero_point_weight); - tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, scales_bias, - zero_point_bias); + scales_weight, zero_point_weight); + tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, + scales_bias, zero_point_bias); tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2, - scales_output, zero_point_output); + scales_output, zero_point_output); tim::vx::TensorSpec input_spec(tim::vx::DataType::UINT8, input_shape, tim::vx::TensorAttribute::INPUT, quant_input); @@ -1047,8 +1050,8 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest1) { std::vector input_data = Quantize(input_data_float, scales_input[0], zero_point_input[0]); - std::vector weight_data = - Quantize(weight_data_float, scales_weight[0], zero_point_input[0]); + std::vector weight_data = Quantize( + weight_data_float, scales_weight[0], zero_point_input[0]); std::vector bias_data = Quantize(bias_data_float, scales_bias[0], zero_point_bias[0]); std::vector golden = @@ -1062,8 +1065,8 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest1) { std::array stride({2, 2}); std::array dilation({1, 1}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -1094,8 +1097,8 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest2) { tim::vx::ShapeType output_shape( {2, 1, weight_shape[3], input_shape[3]}); //whcn - float input_min = -128.5, input_max = 128, weight_min = -128.5, weight_max = 128, - output_min = -127, output_max = 128; + float input_min = -128.5, input_max = 128, weight_min = -128.5, + weight_max = 128, output_min = -127, output_max = 128; std::pair scales_zp; @@ -1115,13 +1118,13 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest2) { std::vector zero_point_output = {scales_zp.second}; tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2, - scales_input, zero_point_input); + scales_input, zero_point_input); tim::vx::Quantization quant_weight(tim::vx::QuantType::ASYMMETRIC, 2, - scales_weight, zero_point_weight); - tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, scales_bias, - zero_point_bias); + scales_weight, zero_point_weight); + tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, + scales_bias, zero_point_bias); tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2, - scales_output, zero_point_output); + scales_output, zero_point_output); tim::vx::TensorSpec input_spec(tim::vx::DataType::UINT8, input_shape, tim::vx::TensorAttribute::INPUT, quant_input); @@ -1151,8 +1154,8 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest2) { std::vector input_data = Quantize(input_data_float, scales_input[0], zero_point_input[0]); - std::vector weight_data = - Quantize(weight_data_float, scales_weight[0], zero_point_input[0]); + std::vector weight_data = Quantize( + weight_data_float, scales_weight[0], zero_point_input[0]); std::vector bias_data = Quantize(bias_data_float, scales_bias[0], zero_point_bias[0]); std::vector golden = @@ -1167,8 +1170,8 @@ TEST(Conv2d, shape_4_2_1_2_uint8_QuantizedTest2) { std::array stride({2, 2}); std::array dilation({1, 1}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -1220,13 +1223,13 @@ TEST(Conv2d, shape_6_3_1_1_uint8_AnisotropicStridesQuantizedTest) { std::vector zero_point_output = {scales_zp.second}; tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2, - scales_input, zero_point_input); + scales_input, zero_point_input); tim::vx::Quantization quant_weight(tim::vx::QuantType::ASYMMETRIC, 2, - scales_weight, zero_point_weight); - tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, scales_bias, - zero_point_bias); + scales_weight, zero_point_weight); + tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, + scales_bias, zero_point_bias); tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2, - scales_output, zero_point_output); + scales_output, zero_point_output); tim::vx::TensorSpec input_spec(tim::vx::DataType::UINT8, input_shape, tim::vx::TensorAttribute::INPUT, quant_input); @@ -1255,8 +1258,8 @@ TEST(Conv2d, shape_6_3_1_1_uint8_AnisotropicStridesQuantizedTest) { std::vector input_data = Quantize(input_data_float, scales_input[0], zero_point_input[0]); - std::vector weight_data = - Quantize(weight_data_float, scales_weight[0], zero_point_input[0]); + std::vector weight_data = Quantize( + weight_data_float, scales_weight[0], zero_point_input[0]); std::vector bias_data = Quantize(bias_data_float, scales_bias[0], zero_point_bias[0]); std::vector golden = @@ -1271,8 +1274,8 @@ TEST(Conv2d, shape_6_3_1_1_uint8_AnisotropicStridesQuantizedTest) { std::array stride({3, 1}); std::array dilation({1, 1}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -1324,13 +1327,13 @@ TEST(Conv2d, shape_9_9_1_1_uint8_DilationQuantizedTest) { std::vector zero_point_output = {scales_zp.second}; tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2, - scales_input, zero_point_input); + scales_input, zero_point_input); tim::vx::Quantization quant_weight(tim::vx::QuantType::ASYMMETRIC, 2, - scales_weight, zero_point_weight); - tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, scales_bias, - zero_point_bias); + scales_weight, zero_point_weight); + tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, + scales_bias, zero_point_bias); tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2, - scales_output, zero_point_output); + scales_output, zero_point_output); tim::vx::TensorSpec input_spec(tim::vx::DataType::UINT8, input_shape, tim::vx::TensorAttribute::INPUT, quant_input); @@ -1362,8 +1365,8 @@ TEST(Conv2d, shape_9_9_1_1_uint8_DilationQuantizedTest) { std::vector input_data = Quantize(input_data_float, scales_input[0], zero_point_input[0]); - std::vector weight_data = - Quantize(weight_data_float, scales_weight[0], zero_point_input[0]); + std::vector weight_data = Quantize( + weight_data_float, scales_weight[0], zero_point_input[0]); std::vector bias_data = Quantize(bias_data_float, scales_bias[0], zero_point_bias[0]); std::vector golden = @@ -1378,8 +1381,8 @@ TEST(Conv2d, shape_9_9_1_1_uint8_DilationQuantizedTest) { std::array stride({1, 1}); std::array dilation({3, 3}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -1431,13 +1434,13 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerTensorTest) { std::vector zero_point_output = {scales_zp.second}; tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2, - scales_input, zero_point_input); + scales_input, zero_point_input); tim::vx::Quantization quant_weight(tim::vx::QuantType::ASYMMETRIC, 2, - scales_weight, zero_point_weight); - tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, scales_bias, - zero_point_bias); + scales_weight, zero_point_weight); + tim::vx::Quantization quant_bias(tim::vx::QuantType::ASYMMETRIC, 2, + scales_bias, zero_point_bias); tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2, - scales_output, zero_point_output); + scales_output, zero_point_output); tim::vx::TensorSpec input_spec(tim::vx::DataType::INT8, input_shape, tim::vx::TensorAttribute::INPUT, quant_input); @@ -1481,8 +1484,8 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerTensorTest) { std::array stride({1, 1}); std::array dilation({1, 1}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -1527,7 +1530,7 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerChannelTest) { std::vector zero_point_weight = {0, 0}; std::vector scales_bias = {scales_input[0] * scales_weight[0], - scales_input[0] * scales_weight[1]}; + scales_input[0] * scales_weight[1]}; std::vector zero_point_bias = {0, 0}; scales_zp = QuantizationParams(output_min, output_max); @@ -1535,13 +1538,13 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerChannelTest) { std::vector zero_point_output = {scales_zp.second}; tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2, - scales_input, zero_point_input); + scales_input, zero_point_input); tim::vx::Quantization quant_weight(tim::vx::QuantType::SYMMETRIC_PER_CHANNEL, - 3, scales_weight, zero_point_weight); + 3, scales_weight, zero_point_weight); tim::vx::Quantization quant_bias(tim::vx::QuantType::SYMMETRIC_PER_CHANNEL, 0, - scales_bias, zero_point_bias); + scales_bias, zero_point_bias); tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2, - scales_output, zero_point_output); + scales_output, zero_point_output); tim::vx::TensorSpec input_spec(tim::vx::DataType::INT8, input_shape, tim::vx::TensorAttribute::INPUT, quant_input); @@ -1583,8 +1586,8 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerChannelTest) { std::array stride({1, 1}); std::array dilation({1, 1}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -1609,12 +1612,12 @@ TEST(Conv2d, shape_3_2_2_1_int8_QuantizedPerChannelTest) { TEST(Conv2d, shape_w_h_128_1_ksize_1_1_stride_2_int8_QuantizedPerChannelTest) { std::map> input_shape_list; input_shape_list[32] = {18, 20, 22, 26, 28, 30, 34, 36, 38, - 42, 44, 46, 50, 52, 54, 58, 60, 62}; + 42, 44, 46, 50, 52, 54, 58, 60, 62}; input_shape_list[63] = {18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62}; input_shape_list[95] = {18, 20, 22, 26, 28, 30, 34, 36, 38, - 42, 44, 46, 50, 52, 54, 58, 60, 62}; + 42, 44, 46, 50, 52, 54, 58, 60, 62}; input_shape_list[96] = {18, 20, 22, 26, 28, 30, 34, 36, 38, - 42, 44, 46, 50, 52, 54, 58, 60, 62}; + 42, 44, 46, 50, 52, 54, 58, 60, 62}; tim::vx::ShapeType input_shape({2, 2, 128, 1}); //whcn tim::vx::ShapeType weight_shape({1, 1, 128, 256}); //whio tim::vx::ShapeType bias_shape({weight_shape[3]}); @@ -1642,13 +1645,13 @@ TEST(Conv2d, shape_w_h_128_1_ksize_1_1_stride_2_int8_QuantizedPerChannelTest) { std::vector zero_point_output = {-1}; tim::vx::Quantization quant_input(tim::vx::QuantType::ASYMMETRIC, 2, - scales_input, zero_point_input); + scales_input, zero_point_input); tim::vx::Quantization quant_weight(tim::vx::QuantType::SYMMETRIC_PER_CHANNEL, - 3, scales_weight, zero_point_weight); + 3, scales_weight, zero_point_weight); tim::vx::Quantization quant_bias(tim::vx::QuantType::SYMMETRIC_PER_CHANNEL, 0, - scales_bias, zero_point_bias); + scales_bias, zero_point_bias); tim::vx::Quantization quant_output(tim::vx::QuantType::ASYMMETRIC, 2, - scales_output, zero_point_output); + scales_output, zero_point_output); uint32_t weight_size = weight_shape[0] * weight_shape[1] * weight_shape[2] * weight_shape[3]; @@ -1699,8 +1702,8 @@ TEST(Conv2d, shape_w_h_128_1_ksize_1_1_stride_2_int8_QuantizedPerChannelTest) { for (uint32_t i = 0; i < golden_size; i++) { golden_float[i] = 129; } - std::vector golden = - Quantize(golden_float, scales_output[0], zero_point_output[0]); + std::vector golden = Quantize( + golden_float, scales_output[0], zero_point_output[0]); auto ctx = tim::vx::Context::Create(); auto graph = ctx->CreateGraph(); @@ -1738,28 +1741,30 @@ TEST(Conv2d, shape_w_h_128_1_ksize_1_1_stride_2_int8_QuantizedPerChannelTest) { } } -TEST(Conv2d, shape_4_2_2_2_int16_DFPQuantizedTest){ +TEST(Conv2d, shape_4_2_2_2_int16_DFPQuantizedTest) { auto ctx = tim::vx::Context::Create(); - if(ctx->isClOnly()) GTEST_SKIP(); + if (ctx->isClOnly()) GTEST_SKIP(); auto graph = ctx->CreateGraph(); tim::vx::ShapeType input_shape({4, 2, 2, 2}); //whcn tim::vx::ShapeType weight_shape({1, 1, 2, 1}); //whio tim::vx::ShapeType bias_shape({weight_shape[3]}); tim::vx::ShapeType output_shape( {4, 2, weight_shape[3], input_shape[3]}); //whcn - int8_t fl_input = 9, fl_weight= 8, fl_output = 8; - tim::vx::Quantization quant_input(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_input); - tim::vx::Quantization quant_weight(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_weight); - tim::vx::Quantization quant_output(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_output); + int8_t fl_input = 9, fl_weight = 8, fl_output = 8; + tim::vx::Quantization quant_input(tim::vx::QuantType::DYNAMIC_FIXED_POINT, + fl_input); + tim::vx::Quantization quant_weight(tim::vx::QuantType::DYNAMIC_FIXED_POINT, + fl_weight); + tim::vx::Quantization quant_output(tim::vx::QuantType::DYNAMIC_FIXED_POINT, + fl_output); tim::vx::TensorSpec input_spec(tim::vx::DataType::INT16, input_shape, - tim::vx::TensorAttribute::INPUT, - quant_input); + tim::vx::TensorAttribute::INPUT, quant_input); tim::vx::TensorSpec weight_spec(tim::vx::DataType::INT16, weight_shape, - tim::vx::TensorAttribute::CONSTANT, - quant_weight); + tim::vx::TensorAttribute::CONSTANT, + quant_weight); tim::vx::TensorSpec output_spec(tim::vx::DataType::INT16, output_shape, - tim::vx::TensorAttribute::OUTPUT, - quant_output); + tim::vx::TensorAttribute::OUTPUT, + quant_output); // Input data float std::vector input_data_float = { @@ -1767,25 +1772,23 @@ TEST(Conv2d, shape_4_2_2_2_int16_DFPQuantizedTest){ 0.5, 1, 1.5, 2, 0.5, 1, 1.5, 2, 0.5, 1, 1.5, 2, 0.5, 1, 1.5, 2}; // weight data float - std::vector weight_data_float= { + std::vector weight_data_float = { 1, 2 // first filter }; //input data(dfp16) - std::vector input_data = { - 256,256,256,256, 512,512,512,512, 256,256,256,256,512,512,512,512, - 256,512,768,1024,256,512,768,1024,256,512,768,1024,256,512,768,1024 - }; + std::vector input_data = {256, 256, 256, 256, 512, 512, 512, 512, + 256, 256, 256, 256, 512, 512, 512, 512, + 256, 512, 768, 1024, 256, 512, 768, 1024, + 256, 512, 768, 1024, 256, 512, 768, 1024}; //weight data(dfp16) - std::vector weight_data = { - 256,512 - }; + std::vector weight_data = {256, 512}; // bias data std::vector bias_data = {0}; //golden std::vector golden = {1.5, 1.5, 1.5, 1.5, 3, 3, 3, 3, 1.5, 3, 4.5, 6, 1.5, 3, 4.5, 6}; - auto input_tensor = graph->CreateTensor(input_spec,input_data.data()); + auto input_tensor = graph->CreateTensor(input_spec, input_data.data()); auto weight_tensor = graph->CreateTensor(weight_spec, weight_data.data()); auto output_tensor = graph->CreateTensor(output_spec); @@ -1793,8 +1796,8 @@ TEST(Conv2d, shape_4_2_2_2_int16_DFPQuantizedTest){ std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -1812,16 +1815,16 @@ TEST(Conv2d, shape_4_2_2_2_int16_DFPQuantizedTest){ } std::vector output(output_size); EXPECT_TRUE(output_tensor->CopyDataFromTensor(output.data())); - //transform output(int16) to fp + //transform output(int16) to fp std::vector f; - for(const auto& q : output){ - f.push_back( q / (float)((int64_t)1 << fl_output)); + for (const auto& q : output) { + f.push_back(q / (float)((int64_t)1 << fl_output)); } EXPECT_EQ(golden, f); } TEST(Conv2d, shape_4_2_1_1_int16_DFPQuantizedTest) { auto ctx = tim::vx::Context::Create(); - if(ctx->isClOnly()) GTEST_SKIP(); + if (ctx->isClOnly()) GTEST_SKIP(); auto graph = ctx->CreateGraph(); tim::vx::ShapeType input_shape({4, 2, 1, 1}); //whcn @@ -1829,32 +1832,34 @@ TEST(Conv2d, shape_4_2_1_1_int16_DFPQuantizedTest) { tim::vx::ShapeType bias_shape({weight_shape[3]}); tim::vx::ShapeType output_shape( {4, 2, weight_shape[3], input_shape[3]}); //whcn - int8_t fl_input = 9, fl_weight = 8, fl_bias = 17,fl_output = 8; + int8_t fl_input = 9, fl_weight = 8, fl_bias = 17, fl_output = 8; - tim::vx::Quantization quant_input(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_input); - tim::vx::Quantization quant_weight(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_weight); - tim::vx::Quantization quant_bias(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_bias); - tim::vx::Quantization quant_output(tim::vx::QuantType::DYNAMIC_FIXED_POINT, fl_output); + tim::vx::Quantization quant_input(tim::vx::QuantType::DYNAMIC_FIXED_POINT, + fl_input); + tim::vx::Quantization quant_weight(tim::vx::QuantType::DYNAMIC_FIXED_POINT, + fl_weight); + tim::vx::Quantization quant_bias(tim::vx::QuantType::DYNAMIC_FIXED_POINT, + fl_bias); + tim::vx::Quantization quant_output(tim::vx::QuantType::DYNAMIC_FIXED_POINT, + fl_output); tim::vx::TensorSpec input_spec(tim::vx::DataType::INT16, input_shape, - tim::vx::TensorAttribute::INPUT, - quant_input); + tim::vx::TensorAttribute::INPUT, quant_input); tim::vx::TensorSpec weight_spec(tim::vx::DataType::INT16, weight_shape, - tim::vx::TensorAttribute::CONSTANT, - quant_weight); + tim::vx::TensorAttribute::CONSTANT, + quant_weight); tim::vx::TensorSpec bias_spec(tim::vx::DataType::INT64, bias_shape, - tim::vx::TensorAttribute::CONSTANT, - quant_bias); + tim::vx::TensorAttribute::CONSTANT, quant_bias); tim::vx::TensorSpec output_spec(tim::vx::DataType::INT16, output_shape, - tim::vx::TensorAttribute::OUTPUT, - quant_output); + tim::vx::TensorAttribute::OUTPUT, + quant_output); // Input data nchw - std::vector input_data_float= { + std::vector input_data_float = { 1, 1, 1, 1, // row = 1 2, 2, 3, 2 // row = 2 }; // weight data oihw - std::vector weight_data_float= { + std::vector weight_data_float = { 1, 2, 3, 4, //first 2x2 filter -1, 1, -1, 1, // second 2x2 filter -1, -1, 1, 1, // third 2x2 filter @@ -1865,24 +1870,18 @@ TEST(Conv2d, shape_4_2_1_1_int16_DFPQuantizedTest) { // nchw std::vector golden = {// first channel - 18, 22, 21, 8, 7, 9, 8, 3, + 18, 22, 21, 8, 7, 9, 8, 3, // second channel - 2, 3, 1, -1, 2, 3, 1, 0, + 2, 3, 1, -1, 2, 3, 1, 0, // third channel - 5, 6, 6, 4, -1, -2, -2, 1}; + 5, 6, 6, 4, -1, -2, -2, 1}; - std::vector input_data = { - 512, 512, 512, 512, - 1024,1024,1536,1024 - }; - std::vector weight_data = { - 256,512,768,1024, - -256,256,-256,256, - -256,-256,256,256 - }; - std::vector bias_data = { - 1< input_data = {512, 512, 512, 512, + 1024, 1024, 1536, 1024}; + std::vector weight_data = {256, 512, 768, 1024, -256, 256, + -256, 256, -256, -256, 256, 256}; + std::vector bias_data = {1 << fl_bias, 2 * (1 << fl_bias), + 3 * (1 << fl_bias)}; auto input_tensor = graph->CreateTensor(input_spec, input_data.data()); auto weight_tensor = graph->CreateTensor(weight_spec, weight_data.data()); @@ -1894,8 +1893,8 @@ TEST(Conv2d, shape_4_2_1_1_int16_DFPQuantizedTest) { std::array stride({1, 1}); std::array dilation({0, 0}); - auto conv2d = graph->CreateOperation( - padding, stride, dilation); + auto conv2d = + graph->CreateOperation(padding, stride, dilation); (*conv2d) .BindInput(input_tensor) .BindInput(weight_tensor) @@ -1916,8 +1915,8 @@ TEST(Conv2d, shape_4_2_1_1_int16_DFPQuantizedTest) { EXPECT_TRUE(output_tensor->CopyDataFromTensor(output.data())); //transform output(int16) to fp std::vector f; - for(const auto& q : output){ - f.push_back( q / (float)((int64_t)1 << fl_output)); + for (const auto& q : output) { + f.push_back(q / (float)((int64_t)1 << fl_output)); } EXPECT_EQ(golden, f); } @@ -1926,7 +1925,7 @@ TEST(Conv2d, kernel_bigger_than_input_SAME) { auto ctx = tim::vx::Context::Create(); auto graph = ctx->CreateGraph(); - tim::vx::ShapeType input_shape({2, 3, 1, 1}); //whcn + tim::vx::ShapeType input_shape({2, 3, 1, 1}); //whcn tim::vx::ShapeType kernel_shape({3, 2, 1, 1}); //whio tim::vx::ShapeType bias_shape({1}); tim::vx::ShapeType output_shape({2, 3, 1, 1}); @@ -1939,13 +1938,16 @@ TEST(Conv2d, kernel_bigger_than_input_SAME) { tim::vx::TensorSpec output_spec(tim::vx::DataType::FLOAT32, output_shape, tim::vx::TensorAttribute::OUTPUT); - std::vector input_data = {1.0f, 3.0f, 4.0f, 2.0f, 2.0f, 3.0f, - }; - std::vector weight = {100.0f, 20.0f, 1.0f, 200.0f, 10.0f, 2.0f, - }; + std::vector input_data = { + 1.0f, 3.0f, 4.0f, 2.0f, 2.0f, 3.0f, + }; + std::vector weight = { + 100.0f, 20.0f, 1.0f, 200.0f, 10.0f, 2.0f, + }; std::vector bias = {500.0f}; - std::vector golden = {567.0f, 1480.0f, 608.0f, 1370.0f, - 543.0f, 760.0f, }; + std::vector golden = { + 567.0f, 1480.0f, 608.0f, 1370.0f, 543.0f, 760.0f, + }; auto input_tensor = graph->CreateTensor(input_spec); auto weight_tensor = graph->CreateTensor(kernel_spec, weight.data()); auto bias_tensor = graph->CreateTensor(bias_spec, bias.data()); @@ -1956,7 +1958,9 @@ TEST(Conv2d, kernel_bigger_than_input_SAME) { auto op = graph->CreateOperation( tim::vx::PadType::SAME, strides, dilations, 0, tim::vx::DataLayout::WHCN, tim::vx::DataLayout::IcWHOc); - (*op).BindInputs({input_tensor, weight_tensor, bias_tensor}).BindOutputs({output_tensor}); + (*op) + .BindInputs({input_tensor, weight_tensor, bias_tensor}) + .BindOutputs({output_tensor}); EXPECT_TRUE(graph->Compile()); diff --git a/third_party/half/ChangeLog.txt b/third_party/half/ChangeLog.txt new file mode 100644 index 0000000..9100b6a --- /dev/null +++ b/third_party/half/ChangeLog.txt @@ -0,0 +1,184 @@ +Release Notes {#changelog} +============= + +1.12.0 release (2017-03-06): +---------------------------- + +- Changed behaviour of `half_cast` to perform conversions to/from `double` + and `long double` directly according to specified rounding mode, without an + intermediate `float` conversion. +- Added `noexcept` specifiers to constructors. +- Fixed minor portability problem with `logb` and `ilogb`. +- Tested for *VC++ 2015*. + + +1.11.0 release (2013-11-16): +---------------------------- + +- Made tie-breaking behaviour in round to nearest configurable by + `HALF_ROUND_TIES_TO_EVEN` macro. +- Completed support for all C++11 mathematical functions even if single- + precision versions from `` are unsupported. +- Fixed inability to disable support for C++11 mathematical functions on + *VC++ 2013*. + + +1.10.0 release (2013-11-09): +---------------------------- + +- Made default rounding mode configurable by `HALF_ROUND_STYLE` macro. +- Added support for non-IEEE single-precision implementations. +- Added `HALF_ENABLE_CPP11_TYPE_TRAITS` preprocessor flag for checking + support for C++11 type traits and TMP features. +- Restricted `half_cast` to support built-in arithmetic types only. +- Changed behaviour of `half_cast` to respect rounding mode when casting + to/from integer types. + + +1.9.2 release (2013-11-01): +--------------------------- + +- Tested for *gcc 4.8*. +- Tested and fixed for *VC++ 2013*. +- Removed unnecessary warnings in *MSVC*. + + +1.9.1 release (2013-08-08): +--------------------------- + +- Fixed problems with older gcc and MSVC versions. +- Small fix to non-C++11 implementations of `remainder` and `remquo`. + + +1.9.0 release (2013-08-07): +--------------------------- + +- Changed behaviour of `nearbyint`, `rint`, `lrint` and `llrint` to use + rounding mode of half-precision implementation (which is + truncating/indeterminate) instead of single-precision rounding mode. +- Added support for more C++11 mathematical functions even if single- + precision versions from `` are unsupported, in particular + `remainder`, `remquo` and `cbrt`. +- Minor implementation changes. + + +1.8.1 release (2013-01-22): +--------------------------- + +- Fixed bug resulting in multiple definitions of the `nanh` function due to + a missing `inline` specification. + + +1.8.0 release (2013-01-19): +--------------------------- + +- Added support for more C++11 mathematical functions even if single- + precision versions from `` are unsupported, in particular + exponential and logarithm functions, hyperbolic area functions and the + hypotenuse function. +- Made `fma` function use default implementation if single-precision version + from `` is not faster and thus `FP_FAST_FMAH` to be defined always. +- Fixed overload resolution issues when invoking certain mathematical + functions by unqualified calls. + + +1.7.0 release (2012-10-26): +--------------------------- + +- Added support for C++11 `noexcept` specifiers. +- Changed C++11 `long long` to be supported on *VC++ 2003* and up. + + +1.6.1 release (2012-09-13): +--------------------------- + +- Made `fma` and `fdim` functions available even if corresponding + single-precision functions are not. + + +1.6.0 release (2012-09-12): +--------------------------- + +- Added `HALF_ENABLE_CPP11_LONG_LONG` to control support for `long long` + integers and corresponding mathematical functions. +- Fixed C++98 compatibility on non-VC compilers. + + +1.5.1 release (2012-08-17): +--------------------------- + +- Recorrected `std::numeric_limits::round_style` to always return + `std::round_indeterminate`, due to overflow-handling deviating from + correct round-toward-zero behaviour. + + +1.5.0 release (2012-08-16): +--------------------------- + +- Added `half_cast` for explicitly casting between half and any type + convertible to/from `float` and allowing the explicit specification of + the rounding mode to use. + + +1.4.0 release (2012-08-12): +--------------------------- + +- Added support for C++11 generalized constant expressions (`constexpr`). + + +1.3.1 release (2012-08-11): +--------------------------- + +- Fixed requirement for `std::signbit` and `std::isnan` (even if C++11 + `` functions disabled) on non-VC compilers. + + +1.3.0 release (2012-08-10): +--------------------------- + +- Made requirement for `` and `static_assert` optional and thus + made the library C++98-compatible. +- Made support for C++11 features user-overridable through explicit + definition of corresponding preprocessor symbols to either 0 or 1. +- Renamed `HALF_ENABLE_HASH` to `HALF_ENABLE_CPP11_HASH` in correspondence + with other C++11 preprocessor symbols. + + +1.2.0 release (2012-08-07): +--------------------------- + +- Added proper preprocessor definitions for `HUGE_VALH` and `FP_FAST_FMAH` + in correspondence with their single-precision counterparts from ``. +- Fixed internal preprocessor macros to be properly undefined after use. + + +1.1.2 release (2012-08-07): +--------------------------- + +- Revised `std::numeric_limits::round_style` to return + `std::round_toward_zero` if the `float` version also does and + `std::round_indeterminate` otherwise. +- Fixed `std::numeric_limits::round_error` to reflect worst-case round + toward zero behaviour. + + +1.1.1 release (2012-08-06): +--------------------------- + +- Fixed `std::numeric_limits::min` to return smallest positive normal + number, instead of subnormal number. +- Fixed `std::numeric_limits::round_style` to return + `std::round_indeterminate` due to mixture of separately rounded + single-precision arithmetics with truncating single-to-half conversions. + + +1.1.0 release (2012-08-06): +--------------------------- + +- Added half-precision literals. + + +1.0.0 release (2012-08-05): +--------------------------- + +- First release. diff --git a/third_party/half/ChangeLog.txt.license b/third_party/half/ChangeLog.txt.license new file mode 100644 index 0000000..771b79e --- /dev/null +++ b/third_party/half/ChangeLog.txt.license @@ -0,0 +1,4 @@ +# +# Copyright (c) 2012-2017 Christian Rau +# SPDX-License-Identifier: MIT +# diff --git a/third_party/half/LICENSE.spdx b/third_party/half/LICENSE.spdx new file mode 100644 index 0000000..d71fa7d --- /dev/null +++ b/third_party/half/LICENSE.spdx @@ -0,0 +1,7 @@ +PackageName: half +SPDXID: SPDXRef-half +FilesAnalyzed: true +PackageLicenseConcluded: MIT +PackageLicenseInfoFromFiles: MIT +PackageLicenseDeclared: MIT +PackageCopyrightText:Copyright (c) 2012-2017 Christian Rau diff --git a/third_party/half/LICENSE.txt b/third_party/half/LICENSE.txt new file mode 100644 index 0000000..9e4618b --- /dev/null +++ b/third_party/half/LICENSE.txt @@ -0,0 +1,21 @@ +The MIT License + +Copyright (c) 2012-2017 Christian Rau + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. diff --git a/third_party/half/README.txt b/third_party/half/README.txt new file mode 100644 index 0000000..3a0960c --- /dev/null +++ b/third_party/half/README.txt @@ -0,0 +1,288 @@ +HALF-PRECISION FLOATING POINT LIBRARY (Version 1.12.0) +------------------------------------------------------ + +This is a C++ header-only library to provide an IEEE 754 conformant 16-bit +half-precision floating point type along with corresponding arithmetic +operators, type conversions and common mathematical functions. It aims for both +efficiency and ease of use, trying to accurately mimic the behaviour of the +builtin floating point types at the best performance possible. + + +INSTALLATION AND REQUIREMENTS +----------------------------- + +Comfortably enough, the library consists of just a single header file +containing all the functionality, which can be directly included by your +projects, without the neccessity to build anything or link to anything. + +Whereas this library is fully C++98-compatible, it can profit from certain +C++11 features. Support for those features is checked automatically at compile +(or rather preprocessing) time, but can be explicitly enabled or disabled by +defining the corresponding preprocessor symbols to either 1 or 0 yourself. This +is useful when the automatic detection fails (for more exotic implementations) +or when a feature should be explicitly disabled: + + - 'long long' integer type for mathematical functions returning 'long long' + results (enabled for VC++ 2003 and newer, gcc and clang, overridable with + 'HALF_ENABLE_CPP11_LONG_LONG'). + + - Static assertions for extended compile-time checks (enabled for VC++ 2010, + gcc 4.3, clang 2.9 and newer, overridable with 'HALF_ENABLE_CPP11_STATIC_ASSERT'). + + - Generalized constant expressions (enabled for VC++ 2015, gcc 4.6, clang 3.1 + and newer, overridable with 'HALF_ENABLE_CPP11_CONSTEXPR'). + + - noexcept exception specifications (enabled for VC++ 2015, gcc 4.6, clang 3.0 + and newer, overridable with 'HALF_ENABLE_CPP11_NOEXCEPT'). + + - User-defined literals for half-precision literals to work (enabled for + VC++ 2015, gcc 4.7, clang 3.1 and newer, overridable with + 'HALF_ENABLE_CPP11_USER_LITERALS'). + + - Type traits and template meta-programming features from + (enabled for VC++ 2010, libstdc++ 4.3, libc++ and newer, overridable with + 'HALF_ENABLE_CPP11_TYPE_TRAITS'). + + - Special integer types from (enabled for VC++ 2010, libstdc++ 4.3, + libc++ and newer, overridable with 'HALF_ENABLE_CPP11_CSTDINT'). + + - Certain C++11 single-precision mathematical functions from for + an improved implementation of their half-precision counterparts to work + (enabled for VC++ 2013, libstdc++ 4.3, libc++ and newer, overridable with + 'HALF_ENABLE_CPP11_CMATH'). + + - Hash functor 'std::hash' from (enabled for VC++ 2010, + libstdc++ 4.3, libc++ and newer, overridable with 'HALF_ENABLE_CPP11_HASH'). + +The library has been tested successfully with Visual C++ 2005-2015, gcc 4.4-4.8 +and clang 3.1. Please contact me if you have any problems, suggestions or even +just success testing it on other platforms. + + +DOCUMENTATION +------------- + +Here follow some general words about the usage of the library and its +implementation. For a complete documentation of its iterface look at the +corresponding website http://half.sourceforge.net. You may also generate the +complete developer documentation from the library's only include file's doxygen +comments, but this is more relevant to developers rather than mere users (for +reasons described below). + +BASIC USAGE + +To make use of the library just include its only header file half.hpp, which +defines all half-precision functionality inside the 'half_float' namespace. The +actual 16-bit half-precision data type is represented by the 'half' type. This +type behaves like the builtin floating point types as much as possible, +supporting the usual arithmetic, comparison and streaming operators, which +makes its use pretty straight-forward: + + using half_float::half; + half a(3.4), b(5); + half c = a * b; + c += 3; + if(c > a) + std::cout << c << std::endl; + +Additionally the 'half_float' namespace also defines half-precision versions +for all mathematical functions of the C++ standard library, which can be used +directly through ADL: + + half a(-3.14159); + half s = sin(abs(a)); + long l = lround(s); + +You may also specify explicit half-precision literals, since the library +provides a user-defined literal inside the 'half_float::literal' namespace, +which you just need to import (assuming support for C++11 user-defined literals): + + using namespace half_float::literal; + half x = 1.0_h; + +Furthermore the library provides proper specializations for +'std::numeric_limits', defining various implementation properties, and +'std::hash' for hashing half-precision numbers (assuming support for C++11 +'std::hash'). Similar to the corresponding preprocessor symbols from +the library also defines the 'HUGE_VALH' constant and maybe the 'FP_FAST_FMAH' +symbol. + +CONVERSIONS AND ROUNDING + +The half is explicitly constructible/convertible from a single-precision float +argument. Thus it is also explicitly constructible/convertible from any type +implicitly convertible to float, but constructing it from types like double or +int will involve the usual warnings arising when implicitly converting those to +float because of the lost precision. On the one hand those warnings are +intentional, because converting those types to half neccessarily also reduces +precision. But on the other hand they are raised for explicit conversions from +those types, when the user knows what he is doing. So if those warnings keep +bugging you, then you won't get around first explicitly converting to float +before converting to half, or use the 'half_cast' described below. In addition +you can also directly assign float values to halfs. + +In contrast to the float-to-half conversion, which reduces precision, the +conversion from half to float (and thus to any other type implicitly +convertible from float) is implicit, because all values represetable with +half-precision are also representable with single-precision. This way the +half-to-float conversion behaves similar to the builtin float-to-double +conversion and all arithmetic expressions involving both half-precision and +single-precision arguments will be of single-precision type. This way you can +also directly use the mathematical functions of the C++ standard library, +though in this case you will invoke the single-precision versions which will +also return single-precision values, which is (even if maybe performing the +exact same computation, see below) not as conceptually clean when working in a +half-precision environment. + +The default rounding mode for conversions from float to half uses truncation +(round toward zero, but mapping overflows to infinity) for rounding values not +representable exactly in half-precision. This is the fastest rounding possible +and is usually sufficient. But by redefining the 'HALF_ROUND_STYLE' +preprocessor symbol (before including half.hpp) this default can be overridden +with one of the other standard rounding modes using their respective constants +or the equivalent values of 'std::float_round_style' (it can even be +synchronized with the underlying single-precision implementation by defining it +to 'std::numeric_limits::round_style'): + + - 'std::round_indeterminate' or -1 for the fastest rounding (default). + + - 'std::round_toward_zero' or 0 for rounding toward zero. + + - std::round_to_nearest' or 1 for rounding to the nearest value. + + - std::round_toward_infinity' or 2 for rounding toward positive infinity. + + - std::round_toward_neg_infinity' or 3 for rounding toward negative infinity. + +In addition to changing the overall default rounding mode one can also use the +'half_cast'. This converts between half and any built-in arithmetic type using +a configurable rounding mode (or the default rounding mode if none is +specified). In addition to a configurable rounding mode, 'half_cast' has +another big difference to a mere 'static_cast': Any conversions are performed +directly using the given rounding mode, without any intermediate conversion +to/from 'float'. This is especially relevant for conversions to integer types, +which don't necessarily truncate anymore. But also for conversions from +'double' or 'long double' this may produce more precise results than a +pre-conversion to 'float' using the single-precision implementation's current +rounding mode would. + + half a = half_cast(4.2); + half b = half_cast::round_style>(4.2f); + assert( half_cast( 0.7_h ) == 1 ); + assert( half_cast( 4097 ) == 4096.0_h ); + assert( half_cast( 4097 ) == 4100.0_h ); + assert( half_cast( std::numeric_limits::min() ) > 0.0_h ); + +When using round to nearest (either as default or through 'half_cast') ties are +by default resolved by rounding them away from zero (and thus equal to the +behaviour of the 'round' function). But by redefining the +'HALF_ROUND_TIES_TO_EVEN' preprocessor symbol to 1 (before including half.hpp) +this default can be changed to the slightly slower but less biased and more +IEEE-conformant behaviour of rounding half-way cases to the nearest even value. + + #define HALF_ROUND_TIES_TO_EVEN 1 + #include + ... + assert( half_cast(3.5_h) + == half_cast(4.5_h) ); + +IMPLEMENTATION + +For performance reasons (and ease of implementation) many of the mathematical +functions provided by the library as well as all arithmetic operations are +actually carried out in single-precision under the hood, calling to the C++ +standard library implementations of those functions whenever appropriate, +meaning the arguments are converted to floats and the result back to half. But +to reduce the conversion overhead as much as possible any temporary values +inside of lengthy expressions are kept in single-precision as long as possible, +while still maintaining a strong half-precision type to the outside world. Only +when finally assigning the value to a half or calling a function that works +directly on halfs is the actual conversion done (or never, when further +converting the result to float. + +This approach has two implications. First of all you have to treat the +library's documentation at http://half.sourceforge.net as a simplified version, +describing the behaviour of the library as if implemented this way. The actual +argument and return types of functions and operators may involve other internal +types (feel free to generate the exact developer documentation from the Doxygen +comments in the library's header file if you really need to). But nevertheless +the behaviour is exactly like specified in the documentation. The other +implication is, that in the presence of rounding errors or over-/underflows +arithmetic expressions may produce different results when compared to +converting to half-precision after each individual operation: + + half a = std::numeric_limits::max() * 2.0_h / 2.0_h; // a = MAX + half b = half(std::numeric_limits::max() * 2.0_h) / 2.0_h; // b = INF + assert( a != b ); + +But this should only be a problem in very few cases. One last word has to be +said when talking about performance. Even with its efforts in reducing +conversion overhead as much as possible, the software half-precision +implementation can most probably not beat the direct use of single-precision +computations. Usually using actual float values for all computations and +temproraries and using halfs only for storage is the recommended way. On the +one hand this somehow makes the provided mathematical functions obsolete +(especially in light of the implicit conversion from half to float), but +nevertheless the goal of this library was to provide a complete and +conceptually clean half-precision implementation, to which the standard +mathematical functions belong, even if usually not needed. + +IEEE CONFORMANCE + +The half type uses the standard IEEE representation with 1 sign bit, 5 exponent +bits and 10 mantissa bits (11 when counting the hidden bit). It supports all +types of special values, like subnormal values, infinity and NaNs. But there +are some limitations to the complete conformance to the IEEE 754 standard: + + - The implementation does not differentiate between signalling and quiet + NaNs, this means operations on halfs are not specified to trap on + signalling NaNs (though they may, see last point). + + - Though arithmetic operations are internally rounded to single-precision + using the underlying single-precision implementation's current rounding + mode, those values are then converted to half-precision using the default + half-precision rounding mode (changed by defining 'HALF_ROUND_STYLE' + accordingly). This mixture of rounding modes is also the reason why + 'std::numeric_limits::round_style' may actually return + 'std::round_indeterminate' when half- and single-precision rounding modes + don't match. + + - Because of internal truncation it may also be that certain single-precision + NaNs will be wrongly converted to half-precision infinity, though this is + very unlikely to happen, since most single-precision implementations don't + tend to only set the lowest bits of a NaN mantissa. + + - The implementation does not provide any floating point exceptions, thus + arithmetic operations or mathematical functions are not specified to invoke + proper floating point exceptions. But due to many functions implemented in + single-precision, those may still invoke floating point exceptions of the + underlying single-precision implementation. + +Some of those points could have been circumvented by controlling the floating +point environment using or implementing a similar exception mechanism. +But this would have required excessive runtime checks giving two high an impact +on performance for something that is rarely ever needed. If you really need to +rely on proper floating point exceptions, it is recommended to explicitly +perform computations using the built-in floating point types to be on the safe +side. In the same way, if you really need to rely on a particular rounding +behaviour, it is recommended to either use single-precision computations and +explicitly convert the result to half-precision using 'half_cast' and +specifying the desired rounding mode, or synchronize the default half-precision +rounding mode to the rounding mode of the single-precision implementation (most +likely 'HALF_ROUND_STYLE=1', 'HALF_ROUND_TIES_TO_EVEN=1'). But this is really +considered an expert-scenario that should be used only when necessary, since +actually working with half-precision usually comes with a certain +tolerance/ignorance of exactness considerations and proper rounding comes with +a certain performance cost. + + +CREDITS AND CONTACT +------------------- + +This library is developed by CHRISTIAN RAU and released under the MIT License +(see LICENSE.txt). If you have any questions or problems with it, feel free to +contact me at rauy@users.sourceforge.net. + +Additional credit goes to JEROEN VAN DER ZIJP for his paper on "Fast Half Float +Conversions", whose algorithms have been used in the library for converting +between half-precision and single-precision values. diff --git a/third_party/half/README.txt.license b/third_party/half/README.txt.license new file mode 100644 index 0000000..771b79e --- /dev/null +++ b/third_party/half/README.txt.license @@ -0,0 +1,4 @@ +# +# Copyright (c) 2012-2017 Christian Rau +# SPDX-License-Identifier: MIT +# diff --git a/third_party/half/half.hpp b/third_party/half/half.hpp new file mode 100644 index 0000000..4e432b9 --- /dev/null +++ b/third_party/half/half.hpp @@ -0,0 +1,3070 @@ +// half - IEEE 754-based half-precision floating point library. +// +// Copyright (c) 2012-2017 Christian Rau +// +// SPDX-License-Identifier: MIT +// +// Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation +// files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, +// modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following conditions: +// +// The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. +// +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE +// WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR +// COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, +// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. + +// Version 1.12.0 + +/// \file +/// Main header file for half precision functionality. + +#ifndef HALF_HALF_HPP +#define HALF_HALF_HPP + +/// Combined gcc version number. +#define HALF_GNUC_VERSION (__GNUC__*100+__GNUC_MINOR__) + +//check C++11 language features +#if defined(__clang__) //clang + #if __has_feature(cxx_static_assert) && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) + #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 + #endif + #if __has_feature(cxx_constexpr) && !defined(HALF_ENABLE_CPP11_CONSTEXPR) + #define HALF_ENABLE_CPP11_CONSTEXPR 1 + #endif + #if __has_feature(cxx_noexcept) && !defined(HALF_ENABLE_CPP11_NOEXCEPT) + #define HALF_ENABLE_CPP11_NOEXCEPT 1 + #endif + #if __has_feature(cxx_user_literals) && !defined(HALF_ENABLE_CPP11_USER_LITERALS) + #define HALF_ENABLE_CPP11_USER_LITERALS 1 + #endif + #if (defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L) && !defined(HALF_ENABLE_CPP11_LONG_LONG) + #define HALF_ENABLE_CPP11_LONG_LONG 1 + #endif +/*#elif defined(__INTEL_COMPILER) //Intel C++ + #if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) ???????? + #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 + #endif + #if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) ???????? + #define HALF_ENABLE_CPP11_CONSTEXPR 1 + #endif + #if __INTEL_COMPILER >= 1300 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) ???????? + #define HALF_ENABLE_CPP11_NOEXCEPT 1 + #endif + #if __INTEL_COMPILER >= 1100 && !defined(HALF_ENABLE_CPP11_LONG_LONG) ???????? + #define HALF_ENABLE_CPP11_LONG_LONG 1 + #endif*/ +#elif defined(__GNUC__) //gcc + #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L + #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) + #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 + #endif + #if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) + #define HALF_ENABLE_CPP11_CONSTEXPR 1 + #endif + #if HALF_GNUC_VERSION >= 406 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) + #define HALF_ENABLE_CPP11_NOEXCEPT 1 + #endif + #if HALF_GNUC_VERSION >= 407 && !defined(HALF_ENABLE_CPP11_USER_LITERALS) + #define HALF_ENABLE_CPP11_USER_LITERALS 1 + #endif + #if !defined(HALF_ENABLE_CPP11_LONG_LONG) + #define HALF_ENABLE_CPP11_LONG_LONG 1 + #endif + #endif +#elif defined(_MSC_VER) //Visual C++ + #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_CONSTEXPR) + #define HALF_ENABLE_CPP11_CONSTEXPR 1 + #endif + #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_NOEXCEPT) + #define HALF_ENABLE_CPP11_NOEXCEPT 1 + #endif + #if _MSC_VER >= 1900 && !defined(HALF_ENABLE_CPP11_USER_LITERALS) + #define HALF_ENABLE_CPP11_USER_LITERALS 1 + #endif + #if _MSC_VER >= 1600 && !defined(HALF_ENABLE_CPP11_STATIC_ASSERT) + #define HALF_ENABLE_CPP11_STATIC_ASSERT 1 + #endif + #if _MSC_VER >= 1310 && !defined(HALF_ENABLE_CPP11_LONG_LONG) + #define HALF_ENABLE_CPP11_LONG_LONG 1 + #endif + #define HALF_POP_WARNINGS 1 + #pragma warning(push) + #pragma warning(disable : 4099 4127 4146) //struct vs class, constant in if, negative unsigned +#endif + +//check C++11 library features +#include +#if defined(_LIBCPP_VERSION) //libc++ + #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103 + #ifndef HALF_ENABLE_CPP11_TYPE_TRAITS + #define HALF_ENABLE_CPP11_TYPE_TRAITS 1 + #endif + #ifndef HALF_ENABLE_CPP11_CSTDINT + #define HALF_ENABLE_CPP11_CSTDINT 1 + #endif + #ifndef HALF_ENABLE_CPP11_CMATH + #define HALF_ENABLE_CPP11_CMATH 1 + #endif + #ifndef HALF_ENABLE_CPP11_HASH + #define HALF_ENABLE_CPP11_HASH 1 + #endif + #endif +#elif defined(__GLIBCXX__) //libstdc++ + #if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103 + #ifdef __clang__ + #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_TYPE_TRAITS) + #define HALF_ENABLE_CPP11_TYPE_TRAITS 1 + #endif + #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CSTDINT) + #define HALF_ENABLE_CPP11_CSTDINT 1 + #endif + #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_CMATH) + #define HALF_ENABLE_CPP11_CMATH 1 + #endif + #if __GLIBCXX__ >= 20080606 && !defined(HALF_ENABLE_CPP11_HASH) + #define HALF_ENABLE_CPP11_HASH 1 + #endif + #else + #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CSTDINT) + #define HALF_ENABLE_CPP11_CSTDINT 1 + #endif + #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_CMATH) + #define HALF_ENABLE_CPP11_CMATH 1 + #endif + #if HALF_GNUC_VERSION >= 403 && !defined(HALF_ENABLE_CPP11_HASH) + #define HALF_ENABLE_CPP11_HASH 1 + #endif + #endif + #endif +#elif defined(_CPPLIB_VER) //Dinkumware/Visual C++ + #if _CPPLIB_VER >= 520 + #ifndef HALF_ENABLE_CPP11_TYPE_TRAITS + #define HALF_ENABLE_CPP11_TYPE_TRAITS 1 + #endif + #ifndef HALF_ENABLE_CPP11_CSTDINT + #define HALF_ENABLE_CPP11_CSTDINT 1 + #endif + #ifndef HALF_ENABLE_CPP11_HASH + #define HALF_ENABLE_CPP11_HASH 1 + #endif + #endif + #if _CPPLIB_VER >= 610 + #ifndef HALF_ENABLE_CPP11_CMATH + #define HALF_ENABLE_CPP11_CMATH 1 + #endif + #endif +#endif +#undef HALF_GNUC_VERSION + +//support constexpr +#if HALF_ENABLE_CPP11_CONSTEXPR + #define HALF_CONSTEXPR constexpr + #define HALF_CONSTEXPR_CONST constexpr +#else + #define HALF_CONSTEXPR + #define HALF_CONSTEXPR_CONST const +#endif + +//support noexcept +#if HALF_ENABLE_CPP11_NOEXCEPT + #define HALF_NOEXCEPT noexcept + #define HALF_NOTHROW noexcept +#else + #define HALF_NOEXCEPT + #define HALF_NOTHROW throw() +#endif + +#include +#include +#include +#include +#include +#include +#include +#if HALF_ENABLE_CPP11_TYPE_TRAITS + #include +#endif +#if HALF_ENABLE_CPP11_CSTDINT + #include +#endif +#if HALF_ENABLE_CPP11_HASH + #include +#endif + + +/// Default rounding mode. +/// This specifies the rounding mode used for all conversions between [half](\ref half_float::half)s and `float`s as well as +/// for the half_cast() if not specifying a rounding mode explicitly. It can be redefined (before including half.hpp) to one +/// of the standard rounding modes using their respective constants or the equivalent values of `std::float_round_style`: +/// +/// `std::float_round_style` | value | rounding +/// ---------------------------------|-------|------------------------- +/// `std::round_indeterminate` | -1 | fastest (default) +/// `std::round_toward_zero` | 0 | toward zero +/// `std::round_to_nearest` | 1 | to nearest +/// `std::round_toward_infinity` | 2 | toward positive infinity +/// `std::round_toward_neg_infinity` | 3 | toward negative infinity +/// +/// By default this is set to `-1` (`std::round_indeterminate`), which uses truncation (round toward zero, but with overflows +/// set to infinity) and is the fastest rounding mode possible. It can even be set to `std::numeric_limits::round_style` +/// to synchronize the rounding mode with that of the underlying single-precision implementation. +#ifndef HALF_ROUND_STYLE + #define HALF_ROUND_STYLE -1 // = std::round_indeterminate +#endif + +/// Tie-breaking behaviour for round to nearest. +/// This specifies if ties in round to nearest should be resolved by rounding to the nearest even value. By default this is +/// defined to `0` resulting in the faster but slightly more biased behaviour of rounding away from zero in half-way cases (and +/// thus equal to the round() function), but can be redefined to `1` (before including half.hpp) if more IEEE-conformant +/// behaviour is needed. +#ifndef HALF_ROUND_TIES_TO_EVEN + #define HALF_ROUND_TIES_TO_EVEN 0 // ties away from zero +#endif + +/// Value signaling overflow. +/// In correspondence with `HUGE_VAL[F|L]` from `` this symbol expands to a positive value signaling the overflow of an +/// operation, in particular it just evaluates to positive infinity. +#define HUGE_VALH std::numeric_limits::infinity() + +/// Fast half-precision fma function. +/// This symbol is only defined if the fma() function generally executes as fast as, or faster than, a separate +/// half-precision multiplication followed by an addition. Due to the internal single-precision implementation of all +/// arithmetic operations, this is in fact always the case. +#define FP_FAST_FMAH 1 + +#ifndef FP_ILOGB0 + #define FP_ILOGB0 INT_MIN +#endif +#ifndef FP_ILOGBNAN + #define FP_ILOGBNAN INT_MAX +#endif +#ifndef FP_SUBNORMAL + #define FP_SUBNORMAL 0 +#endif +#ifndef FP_ZERO + #define FP_ZERO 1 +#endif +#ifndef FP_NAN + #define FP_NAN 2 +#endif +#ifndef FP_INFINITE + #define FP_INFINITE 3 +#endif +#ifndef FP_NORMAL + #define FP_NORMAL 4 +#endif + + +/// Main namespace for half precision functionality. +/// This namespace contains all the functionality provided by the library. +namespace half_float +{ + class half; + +#if HALF_ENABLE_CPP11_USER_LITERALS + /// Library-defined half-precision literals. + /// Import this namespace to enable half-precision floating point literals: + /// ~~~~{.cpp} + /// using namespace half_float::literal; + /// half_float::half = 4.2_h; + /// ~~~~ + namespace literal + { + half operator""_h(long double); + } +#endif + + /// \internal + /// \brief Implementation details. + namespace detail + { + #if HALF_ENABLE_CPP11_TYPE_TRAITS + /// Conditional type. + template struct conditional : std::conditional {}; + + /// Helper for tag dispatching. + template struct bool_type : std::integral_constant {}; + using std::true_type; + using std::false_type; + + /// Type traits for floating point types. + template struct is_float : std::is_floating_point {}; + #else + /// Conditional type. + template struct conditional { typedef T type; }; + template struct conditional { typedef F type; }; + + /// Helper for tag dispatching. + template struct bool_type {}; + typedef bool_type true_type; + typedef bool_type false_type; + + /// Type traits for floating point types. + template struct is_float : false_type {}; + template struct is_float : is_float {}; + template struct is_float : is_float {}; + template struct is_float : is_float {}; + template<> struct is_float : true_type {}; + template<> struct is_float : true_type {}; + template<> struct is_float : true_type {}; + #endif + + /// Type traits for floating point bits. + template struct bits { typedef unsigned char type; }; + template struct bits : bits {}; + template struct bits : bits {}; + template struct bits : bits {}; + + #if HALF_ENABLE_CPP11_CSTDINT + /// Unsigned integer of (at least) 16 bits width. + typedef std::uint_least16_t uint16; + + /// Unsigned integer of (at least) 32 bits width. + template<> struct bits { typedef std::uint_least32_t type; }; + + /// Unsigned integer of (at least) 64 bits width. + template<> struct bits { typedef std::uint_least64_t type; }; + #else + /// Unsigned integer of (at least) 16 bits width. + typedef unsigned short uint16; + + /// Unsigned integer of (at least) 32 bits width. + template<> struct bits : conditional::digits>=32,unsigned int,unsigned long> {}; + + #if HALF_ENABLE_CPP11_LONG_LONG + /// Unsigned integer of (at least) 64 bits width. + template<> struct bits : conditional::digits>=64,unsigned long,unsigned long long> {}; + #else + /// Unsigned integer of (at least) 64 bits width. + template<> struct bits { typedef unsigned long type; }; + #endif + #endif + + /// Tag type for binary construction. + struct binary_t {}; + + /// Tag for binary construction. + HALF_CONSTEXPR_CONST binary_t binary = binary_t(); + + /// Temporary half-precision expression. + /// This class represents a half-precision expression which just stores a single-precision value internally. + struct expr + { + /// Conversion constructor. + /// \param f single-precision value to convert + explicit HALF_CONSTEXPR expr(float f) HALF_NOEXCEPT : value_(f) {} + + /// Conversion to single-precision. + /// \return single precision value representing expression value + HALF_CONSTEXPR operator float() const HALF_NOEXCEPT { return value_; } + + private: + /// Internal expression value stored in single-precision. + float value_; + }; + + /// SFINAE helper for generic half-precision functions. + /// This class template has to be specialized for each valid combination of argument types to provide a corresponding + /// `type` member equivalent to \a T. + /// \tparam T type to return + template struct enable {}; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + template struct enable { typedef T type; }; + + /// Return type for specialized generic 2-argument half-precision functions. + /// This class template has to be specialized for each valid combination of argument types to provide a corresponding + /// `type` member denoting the appropriate return type. + /// \tparam T first argument type + /// \tparam U first argument type + template struct result : enable {}; + template<> struct result { typedef half type; }; + + /// \name Classification helpers + /// \{ + + /// Check for infinity. + /// \tparam T argument type (builtin floating point type) + /// \param arg value to query + /// \retval true if infinity + /// \retval false else + template bool builtin_isinf(T arg) + { + #if HALF_ENABLE_CPP11_CMATH + return std::isinf(arg); + #elif defined(_MSC_VER) + return !::_finite(static_cast(arg)) && !::_isnan(static_cast(arg)); + #else + return arg == std::numeric_limits::infinity() || arg == -std::numeric_limits::infinity(); + #endif + } + + /// Check for NaN. + /// \tparam T argument type (builtin floating point type) + /// \param arg value to query + /// \retval true if not a number + /// \retval false else + template bool builtin_isnan(T arg) + { + #if HALF_ENABLE_CPP11_CMATH + return std::isnan(arg); + #elif defined(_MSC_VER) + return ::_isnan(static_cast(arg)) != 0; + #else + return arg != arg; + #endif + } + + /// Check sign. + /// \tparam T argument type (builtin floating point type) + /// \param arg value to query + /// \retval true if signbit set + /// \retval false else + template bool builtin_signbit(T arg) + { + #if HALF_ENABLE_CPP11_CMATH + return std::signbit(arg); + #else + return arg < T() || (arg == T() && T(1)/arg < T()); + #endif + } + + /// \} + /// \name Conversion + /// \{ + + /// Convert IEEE single-precision to half-precision. + /// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf). + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \param value single-precision value + /// \return binary representation of half-precision value + template uint16 float2half_impl(float value, true_type) + { + typedef bits::type uint32; + uint32 bits;// = *reinterpret_cast(&value); //violating strict aliasing! + std::memcpy(&bits, &value, sizeof(float)); +/* uint16 hbits = (bits>>16) & 0x8000; + bits &= 0x7FFFFFFF; + int exp = bits >> 23; + if(exp == 255) + return hbits | 0x7C00 | (0x3FF&-static_cast((bits&0x7FFFFF)!=0)); + if(exp > 142) + { + if(R == std::round_toward_infinity) + return hbits | 0x7C00 - (hbits>>15); + if(R == std::round_toward_neg_infinity) + return hbits | 0x7BFF + (hbits>>15); + return hbits | 0x7BFF + (R!=std::round_toward_zero); + } + int g, s; + if(exp > 112) + { + g = (bits>>12) & 1; + s = (bits&0xFFF) != 0; + hbits |= ((exp-112)<<10) | ((bits>>13)&0x3FF); + } + else if(exp > 101) + { + int i = 125 - exp; + bits = (bits&0x7FFFFF) | 0x800000; + g = (bits>>i) & 1; + s = (bits&((1L<> (i+1); + } + else + { + g = 0; + s = bits != 0; + } + if(R == std::round_to_nearest) + #if HALF_ROUND_TIES_TO_EVEN + hbits += g & (s|hbits); + #else + hbits += g; + #endif + else if(R == std::round_toward_infinity) + hbits += ~(hbits>>15) & (s|g); + else if(R == std::round_toward_neg_infinity) + hbits += (hbits>>15) & (g|s); +*/ static const uint16 base_table[512] = { + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, + 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0001, 0x0002, 0x0004, 0x0008, 0x0010, 0x0020, 0x0040, 0x0080, 0x0100, + 0x0200, 0x0400, 0x0800, 0x0C00, 0x1000, 0x1400, 0x1800, 0x1C00, 0x2000, 0x2400, 0x2800, 0x2C00, 0x3000, 0x3400, 0x3800, 0x3C00, + 0x4000, 0x4400, 0x4800, 0x4C00, 0x5000, 0x5400, 0x5800, 0x5C00, 0x6000, 0x6400, 0x6800, 0x6C00, 0x7000, 0x7400, 0x7800, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, 0x7C00, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, + 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8000, 0x8001, 0x8002, 0x8004, 0x8008, 0x8010, 0x8020, 0x8040, 0x8080, 0x8100, + 0x8200, 0x8400, 0x8800, 0x8C00, 0x9000, 0x9400, 0x9800, 0x9C00, 0xA000, 0xA400, 0xA800, 0xAC00, 0xB000, 0xB400, 0xB800, 0xBC00, + 0xC000, 0xC400, 0xC800, 0xCC00, 0xD000, 0xD400, 0xD800, 0xDC00, 0xE000, 0xE400, 0xE800, 0xEC00, 0xF000, 0xF400, 0xF800, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, + 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00, 0xFC00 }; + static const unsigned char shift_table[512] = { + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, + 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, + 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, + 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 13 }; + uint16 hbits = base_table[bits>>23] + static_cast((bits&0x7FFFFF)>>shift_table[bits>>23]); + if(R == std::round_to_nearest) + hbits += (((bits&0x7FFFFF)>>(shift_table[bits>>23]-1))|(((bits>>23)&0xFF)==102)) & ((hbits&0x7C00)!=0x7C00) + #if HALF_ROUND_TIES_TO_EVEN + & (((((static_cast(1)<<(shift_table[bits>>23]-1))-1)&bits)!=0)|hbits) + #endif + ; + else if(R == std::round_toward_zero) + hbits -= ((hbits&0x7FFF)==0x7C00) & ~shift_table[bits>>23]; + else if(R == std::round_toward_infinity) + hbits += ((((bits&0x7FFFFF&((static_cast(1)<<(shift_table[bits>>23]))-1))!=0)|(((bits>>23)<=102)& + ((bits>>23)!=0)))&(hbits<0x7C00)) - ((hbits==0xFC00)&((bits>>23)!=511)); + else if(R == std::round_toward_neg_infinity) + hbits += ((((bits&0x7FFFFF&((static_cast(1)<<(shift_table[bits>>23]))-1))!=0)|(((bits>>23)<=358)& + ((bits>>23)!=256)))&(hbits<0xFC00)&(hbits>>15)) - ((hbits==0x7C00)&((bits>>23)!=255)); + return hbits; + } + + /// Convert IEEE double-precision to half-precision. + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \param value double-precision value + /// \return binary representation of half-precision value + template uint16 float2half_impl(double value, true_type) + { + typedef bits::type uint32; + typedef bits::type uint64; + uint64 bits;// = *reinterpret_cast(&value); //violating strict aliasing! + std::memcpy(&bits, &value, sizeof(double)); + uint32 hi = bits >> 32, lo = bits & 0xFFFFFFFF; + uint16 hbits = (hi>>16) & 0x8000; + hi &= 0x7FFFFFFF; + int exp = hi >> 20; + if(exp == 2047) + return hbits | 0x7C00 | (0x3FF&-static_cast((bits&0xFFFFFFFFFFFFF)!=0)); + if(exp > 1038) + { + if(R == std::round_toward_infinity) + return hbits | 0x7C00 - (hbits>>15); + if(R == std::round_toward_neg_infinity) + return hbits | 0x7BFF + (hbits>>15); + return hbits | 0x7BFF + (R!=std::round_toward_zero); + } + int g, s = lo != 0; + if(exp > 1008) + { + g = (hi>>9) & 1; + s |= (hi&0x1FF) != 0; + hbits |= ((exp-1008)<<10) | ((hi>>10)&0x3FF); + } + else if(exp > 997) + { + int i = 1018 - exp; + hi = (hi&0xFFFFF) | 0x100000; + g = (hi>>i) & 1; + s |= (hi&((1L<> (i+1); + } + else + { + g = 0; + s |= hi != 0; + } + if(R == std::round_to_nearest) + #if HALF_ROUND_TIES_TO_EVEN + hbits += g & (s|hbits); + #else + hbits += g; + #endif + else if(R == std::round_toward_infinity) + hbits += ~(hbits>>15) & (s|g); + else if(R == std::round_toward_neg_infinity) + hbits += (hbits>>15) & (g|s); + return hbits; + } + + /// Convert non-IEEE floating point to half-precision. + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \tparam T source type (builtin floating point type) + /// \param value floating point value + /// \return binary representation of half-precision value + template uint16 float2half_impl(T value, ...) + { + uint16 hbits = static_cast(builtin_signbit(value)) << 15; + if(value == T()) + return hbits; + if(builtin_isnan(value)) + return hbits | 0x7FFF; + if(builtin_isinf(value)) + return hbits | 0x7C00; + int exp; + std::frexp(value, &exp); + if(exp > 16) + { + if(R == std::round_toward_infinity) + return hbits | (0x7C00-(hbits>>15)); + else if(R == std::round_toward_neg_infinity) + return hbits | (0x7BFF+(hbits>>15)); + return hbits | (0x7BFF+(R!=std::round_toward_zero)); + } + if(exp < -13) + value = std::ldexp(value, 24); + else + { + value = std::ldexp(value, 11-exp); + hbits |= ((exp+13)<<10); + } + T ival, frac = std::modf(value, &ival); + hbits += static_cast(std::abs(static_cast(ival))); + if(R == std::round_to_nearest) + { + frac = std::abs(frac); + #if HALF_ROUND_TIES_TO_EVEN + hbits += (frac>T(0.5)) | ((frac==T(0.5))&hbits); + #else + hbits += frac >= T(0.5); + #endif + } + else if(R == std::round_toward_infinity) + hbits += frac > T(); + else if(R == std::round_toward_neg_infinity) + hbits += frac < T(); + return hbits; + } + + /// Convert floating point to half-precision. + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \tparam T source type (builtin floating point type) + /// \param value floating point value + /// \return binary representation of half-precision value + template uint16 float2half(T value) + { + return float2half_impl(value, bool_type::is_iec559&&sizeof(typename bits::type)==sizeof(T)>()); + } + + /// Convert integer to half-precision floating point. + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \tparam S `true` if value negative, `false` else + /// \tparam T type to convert (builtin integer type) + /// \param value non-negative integral value + /// \return binary representation of half-precision value + template uint16 int2half_impl(T value) + { + #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_integral::value, "int to half conversion only supports builtin integer types"); + #endif + if(S) + value = -value; + uint16 bits = S << 15; + if(value > 0xFFFF) + { + if(R == std::round_toward_infinity) + bits |= 0x7C00 - S; + else if(R == std::round_toward_neg_infinity) + bits |= 0x7BFF + S; + else + bits |= 0x7BFF + (R!=std::round_toward_zero); + } + else if(value) + { + unsigned int m = value, exp = 24; + for(; m<0x400; m<<=1,--exp) ; + for(; m>0x7FF; m>>=1,++exp) ; + bits |= (exp<<10) + m; + if(exp > 24) + { + if(R == std::round_to_nearest) + bits += (value>>(exp-25)) & 1 + #if HALF_ROUND_TIES_TO_EVEN + & (((((1<<(exp-25))-1)&value)!=0)|bits) + #endif + ; + else if(R == std::round_toward_infinity) + bits += ((value&((1<<(exp-24))-1))!=0) & !S; + else if(R == std::round_toward_neg_infinity) + bits += ((value&((1<<(exp-24))-1))!=0) & S; + } + } + return bits; + } + + /// Convert integer to half-precision floating point. + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \tparam T type to convert (builtin integer type) + /// \param value integral value + /// \return binary representation of half-precision value + template uint16 int2half(T value) + { + return (value<0) ? int2half_impl(value) : int2half_impl(value); + } + + /// Convert half-precision to IEEE single-precision. + /// Credit for this goes to [Jeroen van der Zijp](ftp://ftp.fox-toolkit.org/pub/fasthalffloatconversion.pdf). + /// \param value binary representation of half-precision value + /// \return single-precision value + inline float half2float_impl(uint16 value, float, true_type) + { + typedef bits::type uint32; +/* uint32 bits = static_cast(value&0x8000) << 16; + int abs = value & 0x7FFF; + if(abs) + { + bits |= 0x38000000 << static_cast(abs>=0x7C00); + for(; abs<0x400; abs<<=1,bits-=0x800000) ; + bits += static_cast(abs) << 13; + } +*/ static const uint32 mantissa_table[2048] = { + 0x00000000, 0x33800000, 0x34000000, 0x34400000, 0x34800000, 0x34A00000, 0x34C00000, 0x34E00000, 0x35000000, 0x35100000, 0x35200000, 0x35300000, 0x35400000, 0x35500000, 0x35600000, 0x35700000, + 0x35800000, 0x35880000, 0x35900000, 0x35980000, 0x35A00000, 0x35A80000, 0x35B00000, 0x35B80000, 0x35C00000, 0x35C80000, 0x35D00000, 0x35D80000, 0x35E00000, 0x35E80000, 0x35F00000, 0x35F80000, + 0x36000000, 0x36040000, 0x36080000, 0x360C0000, 0x36100000, 0x36140000, 0x36180000, 0x361C0000, 0x36200000, 0x36240000, 0x36280000, 0x362C0000, 0x36300000, 0x36340000, 0x36380000, 0x363C0000, + 0x36400000, 0x36440000, 0x36480000, 0x364C0000, 0x36500000, 0x36540000, 0x36580000, 0x365C0000, 0x36600000, 0x36640000, 0x36680000, 0x366C0000, 0x36700000, 0x36740000, 0x36780000, 0x367C0000, + 0x36800000, 0x36820000, 0x36840000, 0x36860000, 0x36880000, 0x368A0000, 0x368C0000, 0x368E0000, 0x36900000, 0x36920000, 0x36940000, 0x36960000, 0x36980000, 0x369A0000, 0x369C0000, 0x369E0000, + 0x36A00000, 0x36A20000, 0x36A40000, 0x36A60000, 0x36A80000, 0x36AA0000, 0x36AC0000, 0x36AE0000, 0x36B00000, 0x36B20000, 0x36B40000, 0x36B60000, 0x36B80000, 0x36BA0000, 0x36BC0000, 0x36BE0000, + 0x36C00000, 0x36C20000, 0x36C40000, 0x36C60000, 0x36C80000, 0x36CA0000, 0x36CC0000, 0x36CE0000, 0x36D00000, 0x36D20000, 0x36D40000, 0x36D60000, 0x36D80000, 0x36DA0000, 0x36DC0000, 0x36DE0000, + 0x36E00000, 0x36E20000, 0x36E40000, 0x36E60000, 0x36E80000, 0x36EA0000, 0x36EC0000, 0x36EE0000, 0x36F00000, 0x36F20000, 0x36F40000, 0x36F60000, 0x36F80000, 0x36FA0000, 0x36FC0000, 0x36FE0000, + 0x37000000, 0x37010000, 0x37020000, 0x37030000, 0x37040000, 0x37050000, 0x37060000, 0x37070000, 0x37080000, 0x37090000, 0x370A0000, 0x370B0000, 0x370C0000, 0x370D0000, 0x370E0000, 0x370F0000, + 0x37100000, 0x37110000, 0x37120000, 0x37130000, 0x37140000, 0x37150000, 0x37160000, 0x37170000, 0x37180000, 0x37190000, 0x371A0000, 0x371B0000, 0x371C0000, 0x371D0000, 0x371E0000, 0x371F0000, + 0x37200000, 0x37210000, 0x37220000, 0x37230000, 0x37240000, 0x37250000, 0x37260000, 0x37270000, 0x37280000, 0x37290000, 0x372A0000, 0x372B0000, 0x372C0000, 0x372D0000, 0x372E0000, 0x372F0000, + 0x37300000, 0x37310000, 0x37320000, 0x37330000, 0x37340000, 0x37350000, 0x37360000, 0x37370000, 0x37380000, 0x37390000, 0x373A0000, 0x373B0000, 0x373C0000, 0x373D0000, 0x373E0000, 0x373F0000, + 0x37400000, 0x37410000, 0x37420000, 0x37430000, 0x37440000, 0x37450000, 0x37460000, 0x37470000, 0x37480000, 0x37490000, 0x374A0000, 0x374B0000, 0x374C0000, 0x374D0000, 0x374E0000, 0x374F0000, + 0x37500000, 0x37510000, 0x37520000, 0x37530000, 0x37540000, 0x37550000, 0x37560000, 0x37570000, 0x37580000, 0x37590000, 0x375A0000, 0x375B0000, 0x375C0000, 0x375D0000, 0x375E0000, 0x375F0000, + 0x37600000, 0x37610000, 0x37620000, 0x37630000, 0x37640000, 0x37650000, 0x37660000, 0x37670000, 0x37680000, 0x37690000, 0x376A0000, 0x376B0000, 0x376C0000, 0x376D0000, 0x376E0000, 0x376F0000, + 0x37700000, 0x37710000, 0x37720000, 0x37730000, 0x37740000, 0x37750000, 0x37760000, 0x37770000, 0x37780000, 0x37790000, 0x377A0000, 0x377B0000, 0x377C0000, 0x377D0000, 0x377E0000, 0x377F0000, + 0x37800000, 0x37808000, 0x37810000, 0x37818000, 0x37820000, 0x37828000, 0x37830000, 0x37838000, 0x37840000, 0x37848000, 0x37850000, 0x37858000, 0x37860000, 0x37868000, 0x37870000, 0x37878000, + 0x37880000, 0x37888000, 0x37890000, 0x37898000, 0x378A0000, 0x378A8000, 0x378B0000, 0x378B8000, 0x378C0000, 0x378C8000, 0x378D0000, 0x378D8000, 0x378E0000, 0x378E8000, 0x378F0000, 0x378F8000, + 0x37900000, 0x37908000, 0x37910000, 0x37918000, 0x37920000, 0x37928000, 0x37930000, 0x37938000, 0x37940000, 0x37948000, 0x37950000, 0x37958000, 0x37960000, 0x37968000, 0x37970000, 0x37978000, + 0x37980000, 0x37988000, 0x37990000, 0x37998000, 0x379A0000, 0x379A8000, 0x379B0000, 0x379B8000, 0x379C0000, 0x379C8000, 0x379D0000, 0x379D8000, 0x379E0000, 0x379E8000, 0x379F0000, 0x379F8000, + 0x37A00000, 0x37A08000, 0x37A10000, 0x37A18000, 0x37A20000, 0x37A28000, 0x37A30000, 0x37A38000, 0x37A40000, 0x37A48000, 0x37A50000, 0x37A58000, 0x37A60000, 0x37A68000, 0x37A70000, 0x37A78000, + 0x37A80000, 0x37A88000, 0x37A90000, 0x37A98000, 0x37AA0000, 0x37AA8000, 0x37AB0000, 0x37AB8000, 0x37AC0000, 0x37AC8000, 0x37AD0000, 0x37AD8000, 0x37AE0000, 0x37AE8000, 0x37AF0000, 0x37AF8000, + 0x37B00000, 0x37B08000, 0x37B10000, 0x37B18000, 0x37B20000, 0x37B28000, 0x37B30000, 0x37B38000, 0x37B40000, 0x37B48000, 0x37B50000, 0x37B58000, 0x37B60000, 0x37B68000, 0x37B70000, 0x37B78000, + 0x37B80000, 0x37B88000, 0x37B90000, 0x37B98000, 0x37BA0000, 0x37BA8000, 0x37BB0000, 0x37BB8000, 0x37BC0000, 0x37BC8000, 0x37BD0000, 0x37BD8000, 0x37BE0000, 0x37BE8000, 0x37BF0000, 0x37BF8000, + 0x37C00000, 0x37C08000, 0x37C10000, 0x37C18000, 0x37C20000, 0x37C28000, 0x37C30000, 0x37C38000, 0x37C40000, 0x37C48000, 0x37C50000, 0x37C58000, 0x37C60000, 0x37C68000, 0x37C70000, 0x37C78000, + 0x37C80000, 0x37C88000, 0x37C90000, 0x37C98000, 0x37CA0000, 0x37CA8000, 0x37CB0000, 0x37CB8000, 0x37CC0000, 0x37CC8000, 0x37CD0000, 0x37CD8000, 0x37CE0000, 0x37CE8000, 0x37CF0000, 0x37CF8000, + 0x37D00000, 0x37D08000, 0x37D10000, 0x37D18000, 0x37D20000, 0x37D28000, 0x37D30000, 0x37D38000, 0x37D40000, 0x37D48000, 0x37D50000, 0x37D58000, 0x37D60000, 0x37D68000, 0x37D70000, 0x37D78000, + 0x37D80000, 0x37D88000, 0x37D90000, 0x37D98000, 0x37DA0000, 0x37DA8000, 0x37DB0000, 0x37DB8000, 0x37DC0000, 0x37DC8000, 0x37DD0000, 0x37DD8000, 0x37DE0000, 0x37DE8000, 0x37DF0000, 0x37DF8000, + 0x37E00000, 0x37E08000, 0x37E10000, 0x37E18000, 0x37E20000, 0x37E28000, 0x37E30000, 0x37E38000, 0x37E40000, 0x37E48000, 0x37E50000, 0x37E58000, 0x37E60000, 0x37E68000, 0x37E70000, 0x37E78000, + 0x37E80000, 0x37E88000, 0x37E90000, 0x37E98000, 0x37EA0000, 0x37EA8000, 0x37EB0000, 0x37EB8000, 0x37EC0000, 0x37EC8000, 0x37ED0000, 0x37ED8000, 0x37EE0000, 0x37EE8000, 0x37EF0000, 0x37EF8000, + 0x37F00000, 0x37F08000, 0x37F10000, 0x37F18000, 0x37F20000, 0x37F28000, 0x37F30000, 0x37F38000, 0x37F40000, 0x37F48000, 0x37F50000, 0x37F58000, 0x37F60000, 0x37F68000, 0x37F70000, 0x37F78000, + 0x37F80000, 0x37F88000, 0x37F90000, 0x37F98000, 0x37FA0000, 0x37FA8000, 0x37FB0000, 0x37FB8000, 0x37FC0000, 0x37FC8000, 0x37FD0000, 0x37FD8000, 0x37FE0000, 0x37FE8000, 0x37FF0000, 0x37FF8000, + 0x38000000, 0x38004000, 0x38008000, 0x3800C000, 0x38010000, 0x38014000, 0x38018000, 0x3801C000, 0x38020000, 0x38024000, 0x38028000, 0x3802C000, 0x38030000, 0x38034000, 0x38038000, 0x3803C000, + 0x38040000, 0x38044000, 0x38048000, 0x3804C000, 0x38050000, 0x38054000, 0x38058000, 0x3805C000, 0x38060000, 0x38064000, 0x38068000, 0x3806C000, 0x38070000, 0x38074000, 0x38078000, 0x3807C000, + 0x38080000, 0x38084000, 0x38088000, 0x3808C000, 0x38090000, 0x38094000, 0x38098000, 0x3809C000, 0x380A0000, 0x380A4000, 0x380A8000, 0x380AC000, 0x380B0000, 0x380B4000, 0x380B8000, 0x380BC000, + 0x380C0000, 0x380C4000, 0x380C8000, 0x380CC000, 0x380D0000, 0x380D4000, 0x380D8000, 0x380DC000, 0x380E0000, 0x380E4000, 0x380E8000, 0x380EC000, 0x380F0000, 0x380F4000, 0x380F8000, 0x380FC000, + 0x38100000, 0x38104000, 0x38108000, 0x3810C000, 0x38110000, 0x38114000, 0x38118000, 0x3811C000, 0x38120000, 0x38124000, 0x38128000, 0x3812C000, 0x38130000, 0x38134000, 0x38138000, 0x3813C000, + 0x38140000, 0x38144000, 0x38148000, 0x3814C000, 0x38150000, 0x38154000, 0x38158000, 0x3815C000, 0x38160000, 0x38164000, 0x38168000, 0x3816C000, 0x38170000, 0x38174000, 0x38178000, 0x3817C000, + 0x38180000, 0x38184000, 0x38188000, 0x3818C000, 0x38190000, 0x38194000, 0x38198000, 0x3819C000, 0x381A0000, 0x381A4000, 0x381A8000, 0x381AC000, 0x381B0000, 0x381B4000, 0x381B8000, 0x381BC000, + 0x381C0000, 0x381C4000, 0x381C8000, 0x381CC000, 0x381D0000, 0x381D4000, 0x381D8000, 0x381DC000, 0x381E0000, 0x381E4000, 0x381E8000, 0x381EC000, 0x381F0000, 0x381F4000, 0x381F8000, 0x381FC000, + 0x38200000, 0x38204000, 0x38208000, 0x3820C000, 0x38210000, 0x38214000, 0x38218000, 0x3821C000, 0x38220000, 0x38224000, 0x38228000, 0x3822C000, 0x38230000, 0x38234000, 0x38238000, 0x3823C000, + 0x38240000, 0x38244000, 0x38248000, 0x3824C000, 0x38250000, 0x38254000, 0x38258000, 0x3825C000, 0x38260000, 0x38264000, 0x38268000, 0x3826C000, 0x38270000, 0x38274000, 0x38278000, 0x3827C000, + 0x38280000, 0x38284000, 0x38288000, 0x3828C000, 0x38290000, 0x38294000, 0x38298000, 0x3829C000, 0x382A0000, 0x382A4000, 0x382A8000, 0x382AC000, 0x382B0000, 0x382B4000, 0x382B8000, 0x382BC000, + 0x382C0000, 0x382C4000, 0x382C8000, 0x382CC000, 0x382D0000, 0x382D4000, 0x382D8000, 0x382DC000, 0x382E0000, 0x382E4000, 0x382E8000, 0x382EC000, 0x382F0000, 0x382F4000, 0x382F8000, 0x382FC000, + 0x38300000, 0x38304000, 0x38308000, 0x3830C000, 0x38310000, 0x38314000, 0x38318000, 0x3831C000, 0x38320000, 0x38324000, 0x38328000, 0x3832C000, 0x38330000, 0x38334000, 0x38338000, 0x3833C000, + 0x38340000, 0x38344000, 0x38348000, 0x3834C000, 0x38350000, 0x38354000, 0x38358000, 0x3835C000, 0x38360000, 0x38364000, 0x38368000, 0x3836C000, 0x38370000, 0x38374000, 0x38378000, 0x3837C000, + 0x38380000, 0x38384000, 0x38388000, 0x3838C000, 0x38390000, 0x38394000, 0x38398000, 0x3839C000, 0x383A0000, 0x383A4000, 0x383A8000, 0x383AC000, 0x383B0000, 0x383B4000, 0x383B8000, 0x383BC000, + 0x383C0000, 0x383C4000, 0x383C8000, 0x383CC000, 0x383D0000, 0x383D4000, 0x383D8000, 0x383DC000, 0x383E0000, 0x383E4000, 0x383E8000, 0x383EC000, 0x383F0000, 0x383F4000, 0x383F8000, 0x383FC000, + 0x38400000, 0x38404000, 0x38408000, 0x3840C000, 0x38410000, 0x38414000, 0x38418000, 0x3841C000, 0x38420000, 0x38424000, 0x38428000, 0x3842C000, 0x38430000, 0x38434000, 0x38438000, 0x3843C000, + 0x38440000, 0x38444000, 0x38448000, 0x3844C000, 0x38450000, 0x38454000, 0x38458000, 0x3845C000, 0x38460000, 0x38464000, 0x38468000, 0x3846C000, 0x38470000, 0x38474000, 0x38478000, 0x3847C000, + 0x38480000, 0x38484000, 0x38488000, 0x3848C000, 0x38490000, 0x38494000, 0x38498000, 0x3849C000, 0x384A0000, 0x384A4000, 0x384A8000, 0x384AC000, 0x384B0000, 0x384B4000, 0x384B8000, 0x384BC000, + 0x384C0000, 0x384C4000, 0x384C8000, 0x384CC000, 0x384D0000, 0x384D4000, 0x384D8000, 0x384DC000, 0x384E0000, 0x384E4000, 0x384E8000, 0x384EC000, 0x384F0000, 0x384F4000, 0x384F8000, 0x384FC000, + 0x38500000, 0x38504000, 0x38508000, 0x3850C000, 0x38510000, 0x38514000, 0x38518000, 0x3851C000, 0x38520000, 0x38524000, 0x38528000, 0x3852C000, 0x38530000, 0x38534000, 0x38538000, 0x3853C000, + 0x38540000, 0x38544000, 0x38548000, 0x3854C000, 0x38550000, 0x38554000, 0x38558000, 0x3855C000, 0x38560000, 0x38564000, 0x38568000, 0x3856C000, 0x38570000, 0x38574000, 0x38578000, 0x3857C000, + 0x38580000, 0x38584000, 0x38588000, 0x3858C000, 0x38590000, 0x38594000, 0x38598000, 0x3859C000, 0x385A0000, 0x385A4000, 0x385A8000, 0x385AC000, 0x385B0000, 0x385B4000, 0x385B8000, 0x385BC000, + 0x385C0000, 0x385C4000, 0x385C8000, 0x385CC000, 0x385D0000, 0x385D4000, 0x385D8000, 0x385DC000, 0x385E0000, 0x385E4000, 0x385E8000, 0x385EC000, 0x385F0000, 0x385F4000, 0x385F8000, 0x385FC000, + 0x38600000, 0x38604000, 0x38608000, 0x3860C000, 0x38610000, 0x38614000, 0x38618000, 0x3861C000, 0x38620000, 0x38624000, 0x38628000, 0x3862C000, 0x38630000, 0x38634000, 0x38638000, 0x3863C000, + 0x38640000, 0x38644000, 0x38648000, 0x3864C000, 0x38650000, 0x38654000, 0x38658000, 0x3865C000, 0x38660000, 0x38664000, 0x38668000, 0x3866C000, 0x38670000, 0x38674000, 0x38678000, 0x3867C000, + 0x38680000, 0x38684000, 0x38688000, 0x3868C000, 0x38690000, 0x38694000, 0x38698000, 0x3869C000, 0x386A0000, 0x386A4000, 0x386A8000, 0x386AC000, 0x386B0000, 0x386B4000, 0x386B8000, 0x386BC000, + 0x386C0000, 0x386C4000, 0x386C8000, 0x386CC000, 0x386D0000, 0x386D4000, 0x386D8000, 0x386DC000, 0x386E0000, 0x386E4000, 0x386E8000, 0x386EC000, 0x386F0000, 0x386F4000, 0x386F8000, 0x386FC000, + 0x38700000, 0x38704000, 0x38708000, 0x3870C000, 0x38710000, 0x38714000, 0x38718000, 0x3871C000, 0x38720000, 0x38724000, 0x38728000, 0x3872C000, 0x38730000, 0x38734000, 0x38738000, 0x3873C000, + 0x38740000, 0x38744000, 0x38748000, 0x3874C000, 0x38750000, 0x38754000, 0x38758000, 0x3875C000, 0x38760000, 0x38764000, 0x38768000, 0x3876C000, 0x38770000, 0x38774000, 0x38778000, 0x3877C000, + 0x38780000, 0x38784000, 0x38788000, 0x3878C000, 0x38790000, 0x38794000, 0x38798000, 0x3879C000, 0x387A0000, 0x387A4000, 0x387A8000, 0x387AC000, 0x387B0000, 0x387B4000, 0x387B8000, 0x387BC000, + 0x387C0000, 0x387C4000, 0x387C8000, 0x387CC000, 0x387D0000, 0x387D4000, 0x387D8000, 0x387DC000, 0x387E0000, 0x387E4000, 0x387E8000, 0x387EC000, 0x387F0000, 0x387F4000, 0x387F8000, 0x387FC000, + 0x38000000, 0x38002000, 0x38004000, 0x38006000, 0x38008000, 0x3800A000, 0x3800C000, 0x3800E000, 0x38010000, 0x38012000, 0x38014000, 0x38016000, 0x38018000, 0x3801A000, 0x3801C000, 0x3801E000, + 0x38020000, 0x38022000, 0x38024000, 0x38026000, 0x38028000, 0x3802A000, 0x3802C000, 0x3802E000, 0x38030000, 0x38032000, 0x38034000, 0x38036000, 0x38038000, 0x3803A000, 0x3803C000, 0x3803E000, + 0x38040000, 0x38042000, 0x38044000, 0x38046000, 0x38048000, 0x3804A000, 0x3804C000, 0x3804E000, 0x38050000, 0x38052000, 0x38054000, 0x38056000, 0x38058000, 0x3805A000, 0x3805C000, 0x3805E000, + 0x38060000, 0x38062000, 0x38064000, 0x38066000, 0x38068000, 0x3806A000, 0x3806C000, 0x3806E000, 0x38070000, 0x38072000, 0x38074000, 0x38076000, 0x38078000, 0x3807A000, 0x3807C000, 0x3807E000, + 0x38080000, 0x38082000, 0x38084000, 0x38086000, 0x38088000, 0x3808A000, 0x3808C000, 0x3808E000, 0x38090000, 0x38092000, 0x38094000, 0x38096000, 0x38098000, 0x3809A000, 0x3809C000, 0x3809E000, + 0x380A0000, 0x380A2000, 0x380A4000, 0x380A6000, 0x380A8000, 0x380AA000, 0x380AC000, 0x380AE000, 0x380B0000, 0x380B2000, 0x380B4000, 0x380B6000, 0x380B8000, 0x380BA000, 0x380BC000, 0x380BE000, + 0x380C0000, 0x380C2000, 0x380C4000, 0x380C6000, 0x380C8000, 0x380CA000, 0x380CC000, 0x380CE000, 0x380D0000, 0x380D2000, 0x380D4000, 0x380D6000, 0x380D8000, 0x380DA000, 0x380DC000, 0x380DE000, + 0x380E0000, 0x380E2000, 0x380E4000, 0x380E6000, 0x380E8000, 0x380EA000, 0x380EC000, 0x380EE000, 0x380F0000, 0x380F2000, 0x380F4000, 0x380F6000, 0x380F8000, 0x380FA000, 0x380FC000, 0x380FE000, + 0x38100000, 0x38102000, 0x38104000, 0x38106000, 0x38108000, 0x3810A000, 0x3810C000, 0x3810E000, 0x38110000, 0x38112000, 0x38114000, 0x38116000, 0x38118000, 0x3811A000, 0x3811C000, 0x3811E000, + 0x38120000, 0x38122000, 0x38124000, 0x38126000, 0x38128000, 0x3812A000, 0x3812C000, 0x3812E000, 0x38130000, 0x38132000, 0x38134000, 0x38136000, 0x38138000, 0x3813A000, 0x3813C000, 0x3813E000, + 0x38140000, 0x38142000, 0x38144000, 0x38146000, 0x38148000, 0x3814A000, 0x3814C000, 0x3814E000, 0x38150000, 0x38152000, 0x38154000, 0x38156000, 0x38158000, 0x3815A000, 0x3815C000, 0x3815E000, + 0x38160000, 0x38162000, 0x38164000, 0x38166000, 0x38168000, 0x3816A000, 0x3816C000, 0x3816E000, 0x38170000, 0x38172000, 0x38174000, 0x38176000, 0x38178000, 0x3817A000, 0x3817C000, 0x3817E000, + 0x38180000, 0x38182000, 0x38184000, 0x38186000, 0x38188000, 0x3818A000, 0x3818C000, 0x3818E000, 0x38190000, 0x38192000, 0x38194000, 0x38196000, 0x38198000, 0x3819A000, 0x3819C000, 0x3819E000, + 0x381A0000, 0x381A2000, 0x381A4000, 0x381A6000, 0x381A8000, 0x381AA000, 0x381AC000, 0x381AE000, 0x381B0000, 0x381B2000, 0x381B4000, 0x381B6000, 0x381B8000, 0x381BA000, 0x381BC000, 0x381BE000, + 0x381C0000, 0x381C2000, 0x381C4000, 0x381C6000, 0x381C8000, 0x381CA000, 0x381CC000, 0x381CE000, 0x381D0000, 0x381D2000, 0x381D4000, 0x381D6000, 0x381D8000, 0x381DA000, 0x381DC000, 0x381DE000, + 0x381E0000, 0x381E2000, 0x381E4000, 0x381E6000, 0x381E8000, 0x381EA000, 0x381EC000, 0x381EE000, 0x381F0000, 0x381F2000, 0x381F4000, 0x381F6000, 0x381F8000, 0x381FA000, 0x381FC000, 0x381FE000, + 0x38200000, 0x38202000, 0x38204000, 0x38206000, 0x38208000, 0x3820A000, 0x3820C000, 0x3820E000, 0x38210000, 0x38212000, 0x38214000, 0x38216000, 0x38218000, 0x3821A000, 0x3821C000, 0x3821E000, + 0x38220000, 0x38222000, 0x38224000, 0x38226000, 0x38228000, 0x3822A000, 0x3822C000, 0x3822E000, 0x38230000, 0x38232000, 0x38234000, 0x38236000, 0x38238000, 0x3823A000, 0x3823C000, 0x3823E000, + 0x38240000, 0x38242000, 0x38244000, 0x38246000, 0x38248000, 0x3824A000, 0x3824C000, 0x3824E000, 0x38250000, 0x38252000, 0x38254000, 0x38256000, 0x38258000, 0x3825A000, 0x3825C000, 0x3825E000, + 0x38260000, 0x38262000, 0x38264000, 0x38266000, 0x38268000, 0x3826A000, 0x3826C000, 0x3826E000, 0x38270000, 0x38272000, 0x38274000, 0x38276000, 0x38278000, 0x3827A000, 0x3827C000, 0x3827E000, + 0x38280000, 0x38282000, 0x38284000, 0x38286000, 0x38288000, 0x3828A000, 0x3828C000, 0x3828E000, 0x38290000, 0x38292000, 0x38294000, 0x38296000, 0x38298000, 0x3829A000, 0x3829C000, 0x3829E000, + 0x382A0000, 0x382A2000, 0x382A4000, 0x382A6000, 0x382A8000, 0x382AA000, 0x382AC000, 0x382AE000, 0x382B0000, 0x382B2000, 0x382B4000, 0x382B6000, 0x382B8000, 0x382BA000, 0x382BC000, 0x382BE000, + 0x382C0000, 0x382C2000, 0x382C4000, 0x382C6000, 0x382C8000, 0x382CA000, 0x382CC000, 0x382CE000, 0x382D0000, 0x382D2000, 0x382D4000, 0x382D6000, 0x382D8000, 0x382DA000, 0x382DC000, 0x382DE000, + 0x382E0000, 0x382E2000, 0x382E4000, 0x382E6000, 0x382E8000, 0x382EA000, 0x382EC000, 0x382EE000, 0x382F0000, 0x382F2000, 0x382F4000, 0x382F6000, 0x382F8000, 0x382FA000, 0x382FC000, 0x382FE000, + 0x38300000, 0x38302000, 0x38304000, 0x38306000, 0x38308000, 0x3830A000, 0x3830C000, 0x3830E000, 0x38310000, 0x38312000, 0x38314000, 0x38316000, 0x38318000, 0x3831A000, 0x3831C000, 0x3831E000, + 0x38320000, 0x38322000, 0x38324000, 0x38326000, 0x38328000, 0x3832A000, 0x3832C000, 0x3832E000, 0x38330000, 0x38332000, 0x38334000, 0x38336000, 0x38338000, 0x3833A000, 0x3833C000, 0x3833E000, + 0x38340000, 0x38342000, 0x38344000, 0x38346000, 0x38348000, 0x3834A000, 0x3834C000, 0x3834E000, 0x38350000, 0x38352000, 0x38354000, 0x38356000, 0x38358000, 0x3835A000, 0x3835C000, 0x3835E000, + 0x38360000, 0x38362000, 0x38364000, 0x38366000, 0x38368000, 0x3836A000, 0x3836C000, 0x3836E000, 0x38370000, 0x38372000, 0x38374000, 0x38376000, 0x38378000, 0x3837A000, 0x3837C000, 0x3837E000, + 0x38380000, 0x38382000, 0x38384000, 0x38386000, 0x38388000, 0x3838A000, 0x3838C000, 0x3838E000, 0x38390000, 0x38392000, 0x38394000, 0x38396000, 0x38398000, 0x3839A000, 0x3839C000, 0x3839E000, + 0x383A0000, 0x383A2000, 0x383A4000, 0x383A6000, 0x383A8000, 0x383AA000, 0x383AC000, 0x383AE000, 0x383B0000, 0x383B2000, 0x383B4000, 0x383B6000, 0x383B8000, 0x383BA000, 0x383BC000, 0x383BE000, + 0x383C0000, 0x383C2000, 0x383C4000, 0x383C6000, 0x383C8000, 0x383CA000, 0x383CC000, 0x383CE000, 0x383D0000, 0x383D2000, 0x383D4000, 0x383D6000, 0x383D8000, 0x383DA000, 0x383DC000, 0x383DE000, + 0x383E0000, 0x383E2000, 0x383E4000, 0x383E6000, 0x383E8000, 0x383EA000, 0x383EC000, 0x383EE000, 0x383F0000, 0x383F2000, 0x383F4000, 0x383F6000, 0x383F8000, 0x383FA000, 0x383FC000, 0x383FE000, + 0x38400000, 0x38402000, 0x38404000, 0x38406000, 0x38408000, 0x3840A000, 0x3840C000, 0x3840E000, 0x38410000, 0x38412000, 0x38414000, 0x38416000, 0x38418000, 0x3841A000, 0x3841C000, 0x3841E000, + 0x38420000, 0x38422000, 0x38424000, 0x38426000, 0x38428000, 0x3842A000, 0x3842C000, 0x3842E000, 0x38430000, 0x38432000, 0x38434000, 0x38436000, 0x38438000, 0x3843A000, 0x3843C000, 0x3843E000, + 0x38440000, 0x38442000, 0x38444000, 0x38446000, 0x38448000, 0x3844A000, 0x3844C000, 0x3844E000, 0x38450000, 0x38452000, 0x38454000, 0x38456000, 0x38458000, 0x3845A000, 0x3845C000, 0x3845E000, + 0x38460000, 0x38462000, 0x38464000, 0x38466000, 0x38468000, 0x3846A000, 0x3846C000, 0x3846E000, 0x38470000, 0x38472000, 0x38474000, 0x38476000, 0x38478000, 0x3847A000, 0x3847C000, 0x3847E000, + 0x38480000, 0x38482000, 0x38484000, 0x38486000, 0x38488000, 0x3848A000, 0x3848C000, 0x3848E000, 0x38490000, 0x38492000, 0x38494000, 0x38496000, 0x38498000, 0x3849A000, 0x3849C000, 0x3849E000, + 0x384A0000, 0x384A2000, 0x384A4000, 0x384A6000, 0x384A8000, 0x384AA000, 0x384AC000, 0x384AE000, 0x384B0000, 0x384B2000, 0x384B4000, 0x384B6000, 0x384B8000, 0x384BA000, 0x384BC000, 0x384BE000, + 0x384C0000, 0x384C2000, 0x384C4000, 0x384C6000, 0x384C8000, 0x384CA000, 0x384CC000, 0x384CE000, 0x384D0000, 0x384D2000, 0x384D4000, 0x384D6000, 0x384D8000, 0x384DA000, 0x384DC000, 0x384DE000, + 0x384E0000, 0x384E2000, 0x384E4000, 0x384E6000, 0x384E8000, 0x384EA000, 0x384EC000, 0x384EE000, 0x384F0000, 0x384F2000, 0x384F4000, 0x384F6000, 0x384F8000, 0x384FA000, 0x384FC000, 0x384FE000, + 0x38500000, 0x38502000, 0x38504000, 0x38506000, 0x38508000, 0x3850A000, 0x3850C000, 0x3850E000, 0x38510000, 0x38512000, 0x38514000, 0x38516000, 0x38518000, 0x3851A000, 0x3851C000, 0x3851E000, + 0x38520000, 0x38522000, 0x38524000, 0x38526000, 0x38528000, 0x3852A000, 0x3852C000, 0x3852E000, 0x38530000, 0x38532000, 0x38534000, 0x38536000, 0x38538000, 0x3853A000, 0x3853C000, 0x3853E000, + 0x38540000, 0x38542000, 0x38544000, 0x38546000, 0x38548000, 0x3854A000, 0x3854C000, 0x3854E000, 0x38550000, 0x38552000, 0x38554000, 0x38556000, 0x38558000, 0x3855A000, 0x3855C000, 0x3855E000, + 0x38560000, 0x38562000, 0x38564000, 0x38566000, 0x38568000, 0x3856A000, 0x3856C000, 0x3856E000, 0x38570000, 0x38572000, 0x38574000, 0x38576000, 0x38578000, 0x3857A000, 0x3857C000, 0x3857E000, + 0x38580000, 0x38582000, 0x38584000, 0x38586000, 0x38588000, 0x3858A000, 0x3858C000, 0x3858E000, 0x38590000, 0x38592000, 0x38594000, 0x38596000, 0x38598000, 0x3859A000, 0x3859C000, 0x3859E000, + 0x385A0000, 0x385A2000, 0x385A4000, 0x385A6000, 0x385A8000, 0x385AA000, 0x385AC000, 0x385AE000, 0x385B0000, 0x385B2000, 0x385B4000, 0x385B6000, 0x385B8000, 0x385BA000, 0x385BC000, 0x385BE000, + 0x385C0000, 0x385C2000, 0x385C4000, 0x385C6000, 0x385C8000, 0x385CA000, 0x385CC000, 0x385CE000, 0x385D0000, 0x385D2000, 0x385D4000, 0x385D6000, 0x385D8000, 0x385DA000, 0x385DC000, 0x385DE000, + 0x385E0000, 0x385E2000, 0x385E4000, 0x385E6000, 0x385E8000, 0x385EA000, 0x385EC000, 0x385EE000, 0x385F0000, 0x385F2000, 0x385F4000, 0x385F6000, 0x385F8000, 0x385FA000, 0x385FC000, 0x385FE000, + 0x38600000, 0x38602000, 0x38604000, 0x38606000, 0x38608000, 0x3860A000, 0x3860C000, 0x3860E000, 0x38610000, 0x38612000, 0x38614000, 0x38616000, 0x38618000, 0x3861A000, 0x3861C000, 0x3861E000, + 0x38620000, 0x38622000, 0x38624000, 0x38626000, 0x38628000, 0x3862A000, 0x3862C000, 0x3862E000, 0x38630000, 0x38632000, 0x38634000, 0x38636000, 0x38638000, 0x3863A000, 0x3863C000, 0x3863E000, + 0x38640000, 0x38642000, 0x38644000, 0x38646000, 0x38648000, 0x3864A000, 0x3864C000, 0x3864E000, 0x38650000, 0x38652000, 0x38654000, 0x38656000, 0x38658000, 0x3865A000, 0x3865C000, 0x3865E000, + 0x38660000, 0x38662000, 0x38664000, 0x38666000, 0x38668000, 0x3866A000, 0x3866C000, 0x3866E000, 0x38670000, 0x38672000, 0x38674000, 0x38676000, 0x38678000, 0x3867A000, 0x3867C000, 0x3867E000, + 0x38680000, 0x38682000, 0x38684000, 0x38686000, 0x38688000, 0x3868A000, 0x3868C000, 0x3868E000, 0x38690000, 0x38692000, 0x38694000, 0x38696000, 0x38698000, 0x3869A000, 0x3869C000, 0x3869E000, + 0x386A0000, 0x386A2000, 0x386A4000, 0x386A6000, 0x386A8000, 0x386AA000, 0x386AC000, 0x386AE000, 0x386B0000, 0x386B2000, 0x386B4000, 0x386B6000, 0x386B8000, 0x386BA000, 0x386BC000, 0x386BE000, + 0x386C0000, 0x386C2000, 0x386C4000, 0x386C6000, 0x386C8000, 0x386CA000, 0x386CC000, 0x386CE000, 0x386D0000, 0x386D2000, 0x386D4000, 0x386D6000, 0x386D8000, 0x386DA000, 0x386DC000, 0x386DE000, + 0x386E0000, 0x386E2000, 0x386E4000, 0x386E6000, 0x386E8000, 0x386EA000, 0x386EC000, 0x386EE000, 0x386F0000, 0x386F2000, 0x386F4000, 0x386F6000, 0x386F8000, 0x386FA000, 0x386FC000, 0x386FE000, + 0x38700000, 0x38702000, 0x38704000, 0x38706000, 0x38708000, 0x3870A000, 0x3870C000, 0x3870E000, 0x38710000, 0x38712000, 0x38714000, 0x38716000, 0x38718000, 0x3871A000, 0x3871C000, 0x3871E000, + 0x38720000, 0x38722000, 0x38724000, 0x38726000, 0x38728000, 0x3872A000, 0x3872C000, 0x3872E000, 0x38730000, 0x38732000, 0x38734000, 0x38736000, 0x38738000, 0x3873A000, 0x3873C000, 0x3873E000, + 0x38740000, 0x38742000, 0x38744000, 0x38746000, 0x38748000, 0x3874A000, 0x3874C000, 0x3874E000, 0x38750000, 0x38752000, 0x38754000, 0x38756000, 0x38758000, 0x3875A000, 0x3875C000, 0x3875E000, + 0x38760000, 0x38762000, 0x38764000, 0x38766000, 0x38768000, 0x3876A000, 0x3876C000, 0x3876E000, 0x38770000, 0x38772000, 0x38774000, 0x38776000, 0x38778000, 0x3877A000, 0x3877C000, 0x3877E000, + 0x38780000, 0x38782000, 0x38784000, 0x38786000, 0x38788000, 0x3878A000, 0x3878C000, 0x3878E000, 0x38790000, 0x38792000, 0x38794000, 0x38796000, 0x38798000, 0x3879A000, 0x3879C000, 0x3879E000, + 0x387A0000, 0x387A2000, 0x387A4000, 0x387A6000, 0x387A8000, 0x387AA000, 0x387AC000, 0x387AE000, 0x387B0000, 0x387B2000, 0x387B4000, 0x387B6000, 0x387B8000, 0x387BA000, 0x387BC000, 0x387BE000, + 0x387C0000, 0x387C2000, 0x387C4000, 0x387C6000, 0x387C8000, 0x387CA000, 0x387CC000, 0x387CE000, 0x387D0000, 0x387D2000, 0x387D4000, 0x387D6000, 0x387D8000, 0x387DA000, 0x387DC000, 0x387DE000, + 0x387E0000, 0x387E2000, 0x387E4000, 0x387E6000, 0x387E8000, 0x387EA000, 0x387EC000, 0x387EE000, 0x387F0000, 0x387F2000, 0x387F4000, 0x387F6000, 0x387F8000, 0x387FA000, 0x387FC000, 0x387FE000 }; + static const uint32 exponent_table[64] = { + 0x00000000, 0x00800000, 0x01000000, 0x01800000, 0x02000000, 0x02800000, 0x03000000, 0x03800000, 0x04000000, 0x04800000, 0x05000000, 0x05800000, 0x06000000, 0x06800000, 0x07000000, 0x07800000, + 0x08000000, 0x08800000, 0x09000000, 0x09800000, 0x0A000000, 0x0A800000, 0x0B000000, 0x0B800000, 0x0C000000, 0x0C800000, 0x0D000000, 0x0D800000, 0x0E000000, 0x0E800000, 0x0F000000, 0x47800000, + 0x80000000, 0x80800000, 0x81000000, 0x81800000, 0x82000000, 0x82800000, 0x83000000, 0x83800000, 0x84000000, 0x84800000, 0x85000000, 0x85800000, 0x86000000, 0x86800000, 0x87000000, 0x87800000, + 0x88000000, 0x88800000, 0x89000000, 0x89800000, 0x8A000000, 0x8A800000, 0x8B000000, 0x8B800000, 0x8C000000, 0x8C800000, 0x8D000000, 0x8D800000, 0x8E000000, 0x8E800000, 0x8F000000, 0xC7800000 }; + static const unsigned short offset_table[64] = { + 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, + 0, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024 }; + uint32 bits = mantissa_table[offset_table[value>>10]+(value&0x3FF)] + exponent_table[value>>10]; +// return *reinterpret_cast(&bits); //violating strict aliasing! + float out; + std::memcpy(&out, &bits, sizeof(float)); + return out; + } + + /// Convert half-precision to IEEE double-precision. + /// \param value binary representation of half-precision value + /// \return double-precision value + inline double half2float_impl(uint16 value, double, true_type) + { + typedef bits::type uint32; + typedef bits::type uint64; + uint32 hi = static_cast(value&0x8000) << 16; + int abs = value & 0x7FFF; + if(abs) + { + hi |= 0x3F000000 << static_cast(abs>=0x7C00); + for(; abs<0x400; abs<<=1,hi-=0x100000) ; + hi += static_cast(abs) << 10; + } + uint64 bits = static_cast(hi) << 32; +// return *reinterpret_cast(&bits); //violating strict aliasing! + double out; + std::memcpy(&out, &bits, sizeof(double)); + return out; + } + + /// Convert half-precision to non-IEEE floating point. + /// \tparam T type to convert to (builtin integer type) + /// \param value binary representation of half-precision value + /// \return floating point value + template T half2float_impl(uint16 value, T, ...) + { + T out; + int abs = value & 0x7FFF; + if(abs > 0x7C00) + out = std::numeric_limits::has_quiet_NaN ? std::numeric_limits::quiet_NaN() : T(); + else if(abs == 0x7C00) + out = std::numeric_limits::has_infinity ? std::numeric_limits::infinity() : std::numeric_limits::max(); + else if(abs > 0x3FF) + out = std::ldexp(static_cast((abs&0x3FF)|0x400), (abs>>10)-25); + else + out = std::ldexp(static_cast(abs), -24); + return (value&0x8000) ? -out : out; + } + + /// Convert half-precision to floating point. + /// \tparam T type to convert to (builtin integer type) + /// \param value binary representation of half-precision value + /// \return floating point value + template T half2float(uint16 value) + { + return half2float_impl(value, T(), bool_type::is_iec559&&sizeof(typename bits::type)==sizeof(T)>()); + } + + /// Convert half-precision floating point to integer. + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \tparam E `true` for round to even, `false` for round away from zero + /// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits) + /// \param value binary representation of half-precision value + /// \return integral value + template T half2int_impl(uint16 value) + { + #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_integral::value, "half to int conversion only supports builtin integer types"); + #endif + unsigned int e = value & 0x7FFF; + if(e >= 0x7C00) + return (value&0x8000) ? std::numeric_limits::min() : std::numeric_limits::max(); + if(e < 0x3800) + { + if(R == std::round_toward_infinity) + return T(~(value>>15)&(e!=0)); + else if(R == std::round_toward_neg_infinity) + return -T(value>0x8000); + return T(); + } + unsigned int m = (value&0x3FF) | 0x400; + e >>= 10; + if(e < 25) + { + if(R == std::round_to_nearest) + m += (1<<(24-e)) - (~(m>>(25-e))&E); + else if(R == std::round_toward_infinity) + m += ((value>>15)-1) & ((1<<(25-e))-1U); + else if(R == std::round_toward_neg_infinity) + m += -(value>>15) & ((1<<(25-e))-1U); + m >>= 25 - e; + } + else + m <<= e - 25; + return (value&0x8000) ? -static_cast(m) : static_cast(m); + } + + /// Convert half-precision floating point to integer. + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits) + /// \param value binary representation of half-precision value + /// \return integral value + template T half2int(uint16 value) { return half2int_impl(value); } + + /// Convert half-precision floating point to integer using round-to-nearest-away-from-zero. + /// \tparam T type to convert to (buitlin integer type with at least 16 bits precision, excluding any implicit sign bits) + /// \param value binary representation of half-precision value + /// \return integral value + template T half2int_up(uint16 value) { return half2int_impl(value); } + + /// Round half-precision number to nearest integer value. + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \tparam E `true` for round to even, `false` for round away from zero + /// \param value binary representation of half-precision value + /// \return half-precision bits for nearest integral value + template uint16 round_half_impl(uint16 value) + { + unsigned int e = value & 0x7FFF; + uint16 result = value; + if(e < 0x3C00) + { + result &= 0x8000; + if(R == std::round_to_nearest) + result |= 0x3C00U & -(e>=(0x3800+E)); + else if(R == std::round_toward_infinity) + result |= 0x3C00U & -(~(value>>15)&(e!=0)); + else if(R == std::round_toward_neg_infinity) + result |= 0x3C00U & -(value>0x8000); + } + else if(e < 0x6400) + { + e = 25 - (e>>10); + unsigned int mask = (1<>e)&E); + else if(R == std::round_toward_infinity) + result += mask & ((value>>15)-1); + else if(R == std::round_toward_neg_infinity) + result += mask & -(value>>15); + result &= ~mask; + } + return result; + } + + /// Round half-precision number to nearest integer value. + /// \tparam R rounding mode to use, `std::round_indeterminate` for fastest rounding + /// \param value binary representation of half-precision value + /// \return half-precision bits for nearest integral value + template uint16 round_half(uint16 value) { return round_half_impl(value); } + + /// Round half-precision number to nearest integer value using round-to-nearest-away-from-zero. + /// \param value binary representation of half-precision value + /// \return half-precision bits for nearest integral value + inline uint16 round_half_up(uint16 value) { return round_half_impl(value); } + /// \} + + struct functions; + template struct unary_specialized; + template struct binary_specialized; + template struct half_caster; + } + + /// Half-precision floating point type. + /// This class implements an IEEE-conformant half-precision floating point type with the usual arithmetic operators and + /// conversions. It is implicitly convertible to single-precision floating point, which makes artihmetic expressions and + /// functions with mixed-type operands to be of the most precise operand type. Additionally all arithmetic operations + /// (and many mathematical functions) are carried out in single-precision internally. All conversions from single- to + /// half-precision are done using the library's default rounding mode, but temporary results inside chained arithmetic + /// expressions are kept in single-precision as long as possible (while of course still maintaining a strong half-precision type). + /// + /// According to the C++98/03 definition, the half type is not a POD type. But according to C++11's less strict and + /// extended definitions it is both a standard layout type and a trivially copyable type (even if not a POD type), which + /// means it can be standard-conformantly copied using raw binary copies. But in this context some more words about the + /// actual size of the type. Although the half is representing an IEEE 16-bit type, it does not neccessarily have to be of + /// exactly 16-bits size. But on any reasonable implementation the actual binary representation of this type will most + /// probably not ivolve any additional "magic" or padding beyond the simple binary representation of the underlying 16-bit + /// IEEE number, even if not strictly guaranteed by the standard. But even then it only has an actual size of 16 bits if + /// your C++ implementation supports an unsigned integer type of exactly 16 bits width. But this should be the case on + /// nearly any reasonable platform. + /// + /// So if your C++ implementation is not totally exotic or imposes special alignment requirements, it is a reasonable + /// assumption that the data of a half is just comprised of the 2 bytes of the underlying IEEE representation. + class half + { + friend struct detail::functions; + friend struct detail::unary_specialized; + friend struct detail::binary_specialized; + template friend struct detail::half_caster; + friend class std::numeric_limits; + #if HALF_ENABLE_CPP11_HASH + friend struct std::hash; + #endif + #if HALF_ENABLE_CPP11_USER_LITERALS + friend half literal::operator""_h(long double); + #endif + + public: + /// Default constructor. + /// This initializes the half to 0. Although this does not match the builtin types' default-initialization semantics + /// and may be less efficient than no initialization, it is needed to provide proper value-initialization semantics. + HALF_CONSTEXPR half() HALF_NOEXCEPT : data_() {} + + /// Copy constructor. + /// \tparam T type of concrete half expression + /// \param rhs half expression to copy from + half(detail::expr rhs) : data_(detail::float2half(static_cast(rhs))) {} + + /// Conversion constructor. + /// \param rhs float to convert + explicit half(float rhs) : data_(detail::float2half(rhs)) {} + + /// Conversion to single-precision. + /// \return single precision value representing expression value + operator float() const { return detail::half2float(data_); } + + /// Assignment operator. + /// \tparam T type of concrete half expression + /// \param rhs half expression to copy from + /// \return reference to this half + half& operator=(detail::expr rhs) { return *this = static_cast(rhs); } + + /// Arithmetic assignment. + /// \tparam T type of concrete half expression + /// \param rhs half expression to add + /// \return reference to this half + template typename detail::enable::type operator+=(T rhs) { return *this += static_cast(rhs); } + + /// Arithmetic assignment. + /// \tparam T type of concrete half expression + /// \param rhs half expression to subtract + /// \return reference to this half + template typename detail::enable::type operator-=(T rhs) { return *this -= static_cast(rhs); } + + /// Arithmetic assignment. + /// \tparam T type of concrete half expression + /// \param rhs half expression to multiply with + /// \return reference to this half + template typename detail::enable::type operator*=(T rhs) { return *this *= static_cast(rhs); } + + /// Arithmetic assignment. + /// \tparam T type of concrete half expression + /// \param rhs half expression to divide by + /// \return reference to this half + template typename detail::enable::type operator/=(T rhs) { return *this /= static_cast(rhs); } + + /// Assignment operator. + /// \param rhs single-precision value to copy from + /// \return reference to this half + half& operator=(float rhs) { data_ = detail::float2half(rhs); return *this; } + + /// Arithmetic assignment. + /// \param rhs single-precision value to add + /// \return reference to this half + half& operator+=(float rhs) { data_ = detail::float2half(detail::half2float(data_)+rhs); return *this; } + + /// Arithmetic assignment. + /// \param rhs single-precision value to subtract + /// \return reference to this half + half& operator-=(float rhs) { data_ = detail::float2half(detail::half2float(data_)-rhs); return *this; } + + /// Arithmetic assignment. + /// \param rhs single-precision value to multiply with + /// \return reference to this half + half& operator*=(float rhs) { data_ = detail::float2half(detail::half2float(data_)*rhs); return *this; } + + /// Arithmetic assignment. + /// \param rhs single-precision value to divide by + /// \return reference to this half + half& operator/=(float rhs) { data_ = detail::float2half(detail::half2float(data_)/rhs); return *this; } + + /// Prefix increment. + /// \return incremented half value + half& operator++() { return *this += 1.0f; } + + /// Prefix decrement. + /// \return decremented half value + half& operator--() { return *this -= 1.0f; } + + /// Postfix increment. + /// \return non-incremented half value + half operator++(int) { half out(*this); ++*this; return out; } + + /// Postfix decrement. + /// \return non-decremented half value + half operator--(int) { half out(*this); --*this; return out; } + + private: + /// Rounding mode to use + static const std::float_round_style round_style = (std::float_round_style)(HALF_ROUND_STYLE); + + /// Constructor. + /// \param bits binary representation to set half to + HALF_CONSTEXPR half(detail::binary_t, detail::uint16 bits) HALF_NOEXCEPT : data_(bits) {} + + /// Internal binary representation + detail::uint16 data_; + }; + +#if HALF_ENABLE_CPP11_USER_LITERALS + namespace literal + { + /// Half literal. + /// While this returns an actual half-precision value, half literals can unfortunately not be constant expressions due + /// to rather involved conversions. + /// \param value literal value + /// \return half with given value (if representable) + inline half operator""_h(long double value) { return half(detail::binary, detail::float2half(value)); } + } +#endif + + namespace detail + { + /// Wrapper implementing unspecialized half-precision functions. + struct functions + { + /// Addition implementation. + /// \param x first operand + /// \param y second operand + /// \return Half-precision sum stored in single-precision + static expr plus(float x, float y) { return expr(x+y); } + + /// Subtraction implementation. + /// \param x first operand + /// \param y second operand + /// \return Half-precision difference stored in single-precision + static expr minus(float x, float y) { return expr(x-y); } + + /// Multiplication implementation. + /// \param x first operand + /// \param y second operand + /// \return Half-precision product stored in single-precision + static expr multiplies(float x, float y) { return expr(x*y); } + + /// Division implementation. + /// \param x first operand + /// \param y second operand + /// \return Half-precision quotient stored in single-precision + static expr divides(float x, float y) { return expr(x/y); } + + /// Output implementation. + /// \param out stream to write to + /// \param arg value to write + /// \return reference to stream + template static std::basic_ostream& write(std::basic_ostream &out, float arg) { return out << arg; } + + /// Input implementation. + /// \param in stream to read from + /// \param arg half to read into + /// \return reference to stream + template static std::basic_istream& read(std::basic_istream &in, half &arg) + { + float f; + if(in >> f) + arg = f; + return in; + } + + /// Modulo implementation. + /// \param x first operand + /// \param y second operand + /// \return Half-precision division remainder stored in single-precision + static expr fmod(float x, float y) { return expr(std::fmod(x, y)); } + + /// Remainder implementation. + /// \param x first operand + /// \param y second operand + /// \return Half-precision division remainder stored in single-precision + static expr remainder(float x, float y) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::remainder(x, y)); + #else + if(builtin_isnan(x) || builtin_isnan(y)) + return expr(std::numeric_limits::quiet_NaN()); + float ax = std::fabs(x), ay = std::fabs(y); + if(ax >= 65536.0f || ay < std::ldexp(1.0f, -24)) + return expr(std::numeric_limits::quiet_NaN()); + if(ay >= 65536.0f) + return expr(x); + if(ax == ay) + return expr(builtin_signbit(x) ? -0.0f : 0.0f); + ax = std::fmod(ax, ay+ay); + float y2 = 0.5f * ay; + if(ax > y2) + { + ax -= ay; + if(ax >= y2) + ax -= ay; + } + return expr(builtin_signbit(x) ? -ax : ax); + #endif + } + + /// Remainder implementation. + /// \param x first operand + /// \param y second operand + /// \param quo address to store quotient bits at + /// \return Half-precision division remainder stored in single-precision + static expr remquo(float x, float y, int *quo) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::remquo(x, y, quo)); + #else + if(builtin_isnan(x) || builtin_isnan(y)) + return expr(std::numeric_limits::quiet_NaN()); + bool sign = builtin_signbit(x), qsign = static_cast(sign^builtin_signbit(y)); + float ax = std::fabs(x), ay = std::fabs(y); + if(ax >= 65536.0f || ay < std::ldexp(1.0f, -24)) + return expr(std::numeric_limits::quiet_NaN()); + if(ay >= 65536.0f) + return expr(x); + if(ax == ay) + return *quo = qsign ? -1 : 1, expr(sign ? -0.0f : 0.0f); + ax = std::fmod(ax, 8.0f*ay); + int cquo = 0; + if(ax >= 4.0f * ay) + { + ax -= 4.0f * ay; + cquo += 4; + } + if(ax >= 2.0f * ay) + { + ax -= 2.0f * ay; + cquo += 2; + } + float y2 = 0.5f * ay; + if(ax > y2) + { + ax -= ay; + ++cquo; + if(ax >= y2) + { + ax -= ay; + ++cquo; + } + } + return *quo = qsign ? -cquo : cquo, expr(sign ? -ax : ax); + #endif + } + + /// Positive difference implementation. + /// \param x first operand + /// \param y second operand + /// \return Positive difference stored in single-precision + static expr fdim(float x, float y) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::fdim(x, y)); + #else + return expr((x<=y) ? 0.0f : (x-y)); + #endif + } + + /// Fused multiply-add implementation. + /// \param x first operand + /// \param y second operand + /// \param z third operand + /// \return \a x * \a y + \a z stored in single-precision + static expr fma(float x, float y, float z) + { + #if HALF_ENABLE_CPP11_CMATH && defined(FP_FAST_FMAF) + return expr(std::fma(x, y, z)); + #else + return expr(x*y+z); + #endif + } + + /// Get NaN. + /// \return Half-precision quiet NaN + static half nanh() { return half(binary, 0x7FFF); } + + /// Exponential implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr exp(float arg) { return expr(std::exp(arg)); } + + /// Exponential implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr expm1(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::expm1(arg)); + #else + return expr(static_cast(std::exp(static_cast(arg))-1.0)); + #endif + } + + /// Binary exponential implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr exp2(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::exp2(arg)); + #else + return expr(static_cast(std::exp(arg*0.69314718055994530941723212145818))); + #endif + } + + /// Logarithm implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr log(float arg) { return expr(std::log(arg)); } + + /// Common logarithm implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr log10(float arg) { return expr(std::log10(arg)); } + + /// Logarithm implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr log1p(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::log1p(arg)); + #else + return expr(static_cast(std::log(1.0+arg))); + #endif + } + + /// Binary logarithm implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr log2(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::log2(arg)); + #else + return expr(static_cast(std::log(static_cast(arg))*1.4426950408889634073599246810019)); + #endif + } + + /// Square root implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr sqrt(float arg) { return expr(std::sqrt(arg)); } + + /// Cubic root implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr cbrt(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::cbrt(arg)); + #else + if(builtin_isnan(arg) || builtin_isinf(arg)) + return expr(arg); + return expr(builtin_signbit(arg) ? -static_cast(std::pow(-static_cast(arg), 1.0/3.0)) : + static_cast(std::pow(static_cast(arg), 1.0/3.0))); + #endif + } + + /// Hypotenuse implementation. + /// \param x first argument + /// \param y second argument + /// \return function value stored in single-preicision + static expr hypot(float x, float y) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::hypot(x, y)); + #else + return expr((builtin_isinf(x) || builtin_isinf(y)) ? std::numeric_limits::infinity() : + static_cast(std::sqrt(static_cast(x)*x+static_cast(y)*y))); + #endif + } + + /// Power implementation. + /// \param base value to exponentiate + /// \param exp power to expontiate to + /// \return function value stored in single-preicision + static expr pow(float base, float exp) { return expr(std::pow(base, exp)); } + + /// Sine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr sin(float arg) { return expr(std::sin(arg)); } + + /// Cosine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr cos(float arg) { return expr(std::cos(arg)); } + + /// Tan implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr tan(float arg) { return expr(std::tan(arg)); } + + /// Arc sine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr asin(float arg) { return expr(std::asin(arg)); } + + /// Arc cosine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr acos(float arg) { return expr(std::acos(arg)); } + + /// Arc tangent implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr atan(float arg) { return expr(std::atan(arg)); } + + /// Arc tangent implementation. + /// \param x first argument + /// \param y second argument + /// \return function value stored in single-preicision + static expr atan2(float x, float y) { return expr(std::atan2(x, y)); } + + /// Hyperbolic sine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr sinh(float arg) { return expr(std::sinh(arg)); } + + /// Hyperbolic cosine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr cosh(float arg) { return expr(std::cosh(arg)); } + + /// Hyperbolic tangent implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr tanh(float arg) { return expr(std::tanh(arg)); } + + /// Hyperbolic area sine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr asinh(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::asinh(arg)); + #else + return expr((arg==-std::numeric_limits::infinity()) ? arg : static_cast(std::log(arg+std::sqrt(arg*arg+1.0)))); + #endif + } + + /// Hyperbolic area cosine implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr acosh(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::acosh(arg)); + #else + return expr((arg<-1.0f) ? std::numeric_limits::quiet_NaN() : static_cast(std::log(arg+std::sqrt(arg*arg-1.0)))); + #endif + } + + /// Hyperbolic area tangent implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr atanh(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::atanh(arg)); + #else + return expr(static_cast(0.5*std::log((1.0+arg)/(1.0-arg)))); + #endif + } + + /// Error function implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr erf(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::erf(arg)); + #else + return expr(static_cast(erf(static_cast(arg)))); + #endif + } + + /// Complementary implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr erfc(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::erfc(arg)); + #else + return expr(static_cast(1.0-erf(static_cast(arg)))); + #endif + } + + /// Gamma logarithm implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr lgamma(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::lgamma(arg)); + #else + if(builtin_isinf(arg)) + return expr(std::numeric_limits::infinity()); + if(arg < 0.0f) + { + float i, f = std::modf(-arg, &i); + if(f == 0.0f) + return expr(std::numeric_limits::infinity()); + return expr(static_cast(1.1447298858494001741434273513531- + std::log(std::abs(std::sin(3.1415926535897932384626433832795*f)))-lgamma(1.0-arg))); + } + return expr(static_cast(lgamma(static_cast(arg)))); + #endif + } + + /// Gamma implementation. + /// \param arg function argument + /// \return function value stored in single-preicision + static expr tgamma(float arg) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::tgamma(arg)); + #else + if(arg == 0.0f) + return builtin_signbit(arg) ? expr(-std::numeric_limits::infinity()) : expr(std::numeric_limits::infinity()); + if(arg < 0.0f) + { + float i, f = std::modf(-arg, &i); + if(f == 0.0f) + return expr(std::numeric_limits::quiet_NaN()); + double value = 3.1415926535897932384626433832795 / (std::sin(3.1415926535897932384626433832795*f)*std::exp(lgamma(1.0-arg))); + return expr(static_cast((std::fmod(i, 2.0f)==0.0f) ? -value : value)); + } + if(builtin_isinf(arg)) + return expr(arg); + return expr(static_cast(std::exp(lgamma(static_cast(arg))))); + #endif + } + + /// Floor implementation. + /// \param arg value to round + /// \return rounded value + static half floor(half arg) { return half(binary, round_half(arg.data_)); } + + /// Ceiling implementation. + /// \param arg value to round + /// \return rounded value + static half ceil(half arg) { return half(binary, round_half(arg.data_)); } + + /// Truncation implementation. + /// \param arg value to round + /// \return rounded value + static half trunc(half arg) { return half(binary, round_half(arg.data_)); } + + /// Nearest integer implementation. + /// \param arg value to round + /// \return rounded value + static half round(half arg) { return half(binary, round_half_up(arg.data_)); } + + /// Nearest integer implementation. + /// \param arg value to round + /// \return rounded value + static long lround(half arg) { return detail::half2int_up(arg.data_); } + + /// Nearest integer implementation. + /// \param arg value to round + /// \return rounded value + static half rint(half arg) { return half(binary, round_half(arg.data_)); } + + /// Nearest integer implementation. + /// \param arg value to round + /// \return rounded value + static long lrint(half arg) { return detail::half2int(arg.data_); } + + #if HALF_ENABLE_CPP11_LONG_LONG + /// Nearest integer implementation. + /// \param arg value to round + /// \return rounded value + static long long llround(half arg) { return detail::half2int_up(arg.data_); } + + /// Nearest integer implementation. + /// \param arg value to round + /// \return rounded value + static long long llrint(half arg) { return detail::half2int(arg.data_); } + #endif + + /// Decompression implementation. + /// \param arg number to decompress + /// \param exp address to store exponent at + /// \return normalized significant + static half frexp(half arg, int *exp) + { + int m = arg.data_ & 0x7FFF, e = -14; + if(m >= 0x7C00 || !m) + return *exp = 0, arg; + for(; m<0x400; m<<=1,--e) ; + return *exp = e+(m>>10), half(binary, (arg.data_&0x8000)|0x3800|(m&0x3FF)); + } + + /// Decompression implementation. + /// \param arg number to decompress + /// \param iptr address to store integer part at + /// \return fractional part + static half modf(half arg, half *iptr) + { + unsigned int e = arg.data_ & 0x7FFF; + if(e >= 0x6400) + return *iptr = arg, half(binary, arg.data_&(0x8000U|-(e>0x7C00))); + if(e < 0x3C00) + return iptr->data_ = arg.data_ & 0x8000, arg; + e >>= 10; + unsigned int mask = (1<<(25-e)) - 1, m = arg.data_ & mask; + iptr->data_ = arg.data_ & ~mask; + if(!m) + return half(binary, arg.data_&0x8000); + for(; m<0x400; m<<=1,--e) ; + return half(binary, static_cast((arg.data_&0x8000)|(e<<10)|(m&0x3FF))); + } + + /// Scaling implementation. + /// \param arg number to scale + /// \param exp power of two to scale by + /// \return scaled number + static half scalbln(half arg, long exp) + { + unsigned int m = arg.data_ & 0x7FFF; + if(m >= 0x7C00 || !m) + return arg; + for(; m<0x400; m<<=1,--exp) ; + exp += m >> 10; + uint16 value = arg.data_ & 0x8000; + if(exp > 30) + { + if(half::round_style == std::round_toward_zero) + value |= 0x7BFF; + else if(half::round_style == std::round_toward_infinity) + value |= 0x7C00 - (value>>15); + else if(half::round_style == std::round_toward_neg_infinity) + value |= 0x7BFF + (value>>15); + else + value |= 0x7C00; + } + else if(exp > 0) + value |= (exp<<10) | (m&0x3FF); + else if(exp > -11) + { + m = (m&0x3FF) | 0x400; + if(half::round_style == std::round_to_nearest) + { + m += 1 << -exp; + #if HALF_ROUND_TIES_TO_EVEN + m -= (m>>(1-exp)) & 1; + #endif + } + else if(half::round_style == std::round_toward_infinity) + m += ((value>>15)-1) & ((1<<(1-exp))-1U); + else if(half::round_style == std::round_toward_neg_infinity) + m += -(value>>15) & ((1<<(1-exp))-1U); + value |= m >> (1-exp); + } + else if(half::round_style == std::round_toward_infinity) + value -= (value>>15) - 1; + else if(half::round_style == std::round_toward_neg_infinity) + value += value >> 15; + return half(binary, value); + } + + /// Exponent implementation. + /// \param arg number to query + /// \return floating point exponent + static int ilogb(half arg) + { + int abs = arg.data_ & 0x7FFF; + if(!abs) + return FP_ILOGB0; + if(abs < 0x7C00) + { + int exp = (abs>>10) - 15; + if(abs < 0x400) + for(; abs<0x200; abs<<=1,--exp) ; + return exp; + } + if(abs > 0x7C00) + return FP_ILOGBNAN; + return INT_MAX; + } + + /// Exponent implementation. + /// \param arg number to query + /// \return floating point exponent + static half logb(half arg) + { + int abs = arg.data_ & 0x7FFF; + if(!abs) + return half(binary, 0xFC00); + if(abs < 0x7C00) + { + int exp = (abs>>10) - 15; + if(abs < 0x400) + for(; abs<0x200; abs<<=1,--exp) ; + uint16 bits = (exp<0) << 15; + if(exp) + { + unsigned int m = std::abs(exp) << 6, e = 18; + for(; m<0x400; m<<=1,--e) ; + bits |= (e<<10) + m; + } + return half(binary, bits); + } + if(abs > 0x7C00) + return arg; + return half(binary, 0x7C00); + } + + /// Enumeration implementation. + /// \param from number to increase/decrease + /// \param to direction to enumerate into + /// \return next representable number + static half nextafter(half from, half to) + { + uint16 fabs = from.data_ & 0x7FFF, tabs = to.data_ & 0x7FFF; + if(fabs > 0x7C00) + return from; + if(tabs > 0x7C00 || from.data_ == to.data_ || !(fabs|tabs)) + return to; + if(!fabs) + return half(binary, (to.data_&0x8000)+1); + bool lt = ((fabs==from.data_) ? static_cast(fabs) : -static_cast(fabs)) < + ((tabs==to.data_) ? static_cast(tabs) : -static_cast(tabs)); + return half(binary, from.data_+(((from.data_>>15)^static_cast(lt))<<1)-1); + } + + /// Enumeration implementation. + /// \param from number to increase/decrease + /// \param to direction to enumerate into + /// \return next representable number + static half nexttoward(half from, long double to) + { + if(isnan(from)) + return from; + long double lfrom = static_cast(from); + if(builtin_isnan(to) || lfrom == to) + return half(static_cast(to)); + if(!(from.data_&0x7FFF)) + return half(binary, (static_cast(builtin_signbit(to))<<15)+1); + return half(binary, from.data_+(((from.data_>>15)^static_cast(lfrom0x3FF) ? ((abs>=0x7C00) ? ((abs>0x7C00) ? FP_NAN : FP_INFINITE) : FP_NORMAL) :FP_SUBNORMAL) : FP_ZERO; + } + + /// Classification implementation. + /// \param arg value to classify + /// \retval true if finite number + /// \retval false else + static bool isfinite(half arg) { return (arg.data_&0x7C00) != 0x7C00; } + + /// Classification implementation. + /// \param arg value to classify + /// \retval true if infinite number + /// \retval false else + static bool isinf(half arg) { return (arg.data_&0x7FFF) == 0x7C00; } + + /// Classification implementation. + /// \param arg value to classify + /// \retval true if not a number + /// \retval false else + static bool isnan(half arg) { return (arg.data_&0x7FFF) > 0x7C00; } + + /// Classification implementation. + /// \param arg value to classify + /// \retval true if normal number + /// \retval false else + static bool isnormal(half arg) { return ((arg.data_&0x7C00)!=0) & ((arg.data_&0x7C00)!=0x7C00); } + + /// Sign bit implementation. + /// \param arg value to check + /// \retval true if signed + /// \retval false if unsigned + static bool signbit(half arg) { return (arg.data_&0x8000) != 0; } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if operands equal + /// \retval false else + static bool isequal(half x, half y) { return (x.data_==y.data_ || !((x.data_|y.data_)&0x7FFF)) && !isnan(x); } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if operands not equal + /// \retval false else + static bool isnotequal(half x, half y) { return (x.data_!=y.data_ && ((x.data_|y.data_)&0x7FFF)) || isnan(x); } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x > \a y + /// \retval false else + static bool isgreater(half x, half y) + { + int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; + return xabs<=0x7C00 && yabs<=0x7C00 && (((xabs==x.data_) ? xabs : -xabs) > ((yabs==y.data_) ? yabs : -yabs)); + } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x >= \a y + /// \retval false else + static bool isgreaterequal(half x, half y) + { + int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; + return xabs<=0x7C00 && yabs<=0x7C00 && (((xabs==x.data_) ? xabs : -xabs) >= ((yabs==y.data_) ? yabs : -yabs)); + } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x < \a y + /// \retval false else + static bool isless(half x, half y) + { + int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; + return xabs<=0x7C00 && yabs<=0x7C00 && (((xabs==x.data_) ? xabs : -xabs) < ((yabs==y.data_) ? yabs : -yabs)); + } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x <= \a y + /// \retval false else + static bool islessequal(half x, half y) + { + int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; + return xabs<=0x7C00 && yabs<=0x7C00 && (((xabs==x.data_) ? xabs : -xabs) <= ((yabs==y.data_) ? yabs : -yabs)); + } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if either \a x > \a y nor \a x < \a y + /// \retval false else + static bool islessgreater(half x, half y) + { + int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; + if(xabs > 0x7C00 || yabs > 0x7C00) + return false; + int a = (xabs==x.data_) ? xabs : -xabs, b = (yabs==y.data_) ? yabs : -yabs; + return a < b || a > b; + } + + /// Comparison implementation. + /// \param x first operand + /// \param y second operand + /// \retval true if operand unordered + /// \retval false else + static bool isunordered(half x, half y) { return isnan(x) || isnan(y); } + + private: + static double erf(double arg) + { + if(builtin_isinf(arg)) + return (arg<0.0) ? -1.0 : 1.0; + double x2 = arg * arg, ax2 = 0.147 * x2, value = std::sqrt(1.0-std::exp(-x2*(1.2732395447351626861510701069801+ax2)/(1.0+ax2))); + return builtin_signbit(arg) ? -value : value; + } + + static double lgamma(double arg) + { + double v = 1.0; + for(; arg<8.0; ++arg) v *= arg; + double w = 1.0 / (arg*arg); + return (((((((-0.02955065359477124183006535947712*w+0.00641025641025641025641025641026)*w+ + -0.00191752691752691752691752691753)*w+8.4175084175084175084175084175084e-4)*w+ + -5.952380952380952380952380952381e-4)*w+7.9365079365079365079365079365079e-4)*w+ + -0.00277777777777777777777777777778)*w+0.08333333333333333333333333333333)/arg + + 0.91893853320467274178032973640562 - std::log(v) - arg + (arg-0.5) * std::log(arg); + } + }; + + /// Wrapper for unary half-precision functions needing specialization for individual argument types. + /// \tparam T argument type + template struct unary_specialized + { + /// Negation implementation. + /// \param arg value to negate + /// \return negated value + static HALF_CONSTEXPR half negate(half arg) { return half(binary, arg.data_^0x8000); } + + /// Absolute value implementation. + /// \param arg function argument + /// \return absolute value + static half fabs(half arg) { return half(binary, arg.data_&0x7FFF); } + }; + template<> struct unary_specialized + { + static HALF_CONSTEXPR expr negate(float arg) { return expr(-arg); } + static expr fabs(float arg) { return expr(std::fabs(arg)); } + }; + + /// Wrapper for binary half-precision functions needing specialization for individual argument types. + /// \tparam T first argument type + /// \tparam U first argument type + template struct binary_specialized + { + /// Minimum implementation. + /// \param x first operand + /// \param y second operand + /// \return minimum value + static expr fmin(float x, float y) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::fmin(x, y)); + #else + if(builtin_isnan(x)) + return expr(y); + if(builtin_isnan(y)) + return expr(x); + return expr(std::min(x, y)); + #endif + } + + /// Maximum implementation. + /// \param x first operand + /// \param y second operand + /// \return maximum value + static expr fmax(float x, float y) + { + #if HALF_ENABLE_CPP11_CMATH + return expr(std::fmax(x, y)); + #else + if(builtin_isnan(x)) + return expr(y); + if(builtin_isnan(y)) + return expr(x); + return expr(std::max(x, y)); + #endif + } + }; + template<> struct binary_specialized + { + static half fmin(half x, half y) + { + int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; + if(xabs > 0x7C00) + return y; + if(yabs > 0x7C00) + return x; + return (((xabs==x.data_) ? xabs : -xabs) > ((yabs==y.data_) ? yabs : -yabs)) ? y : x; + } + static half fmax(half x, half y) + { + int xabs = x.data_ & 0x7FFF, yabs = y.data_ & 0x7FFF; + if(xabs > 0x7C00) + return y; + if(yabs > 0x7C00) + return x; + return (((xabs==x.data_) ? xabs : -xabs) < ((yabs==y.data_) ? yabs : -yabs)) ? y : x; + } + }; + + /// Helper class for half casts. + /// This class template has to be specialized for all valid cast argument to define an appropriate static `cast` member + /// function and a corresponding `type` member denoting its return type. + /// \tparam T destination type + /// \tparam U source type + /// \tparam R rounding mode to use + template struct half_caster {}; + template struct half_caster + { + #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_arithmetic::value, "half_cast from non-arithmetic type unsupported"); + #endif + + static half cast(U arg) { return cast_impl(arg, is_float()); }; + + private: + static half cast_impl(U arg, true_type) { return half(binary, float2half(arg)); } + static half cast_impl(U arg, false_type) { return half(binary, int2half(arg)); } + }; + template struct half_caster + { + #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_arithmetic::value, "half_cast to non-arithmetic type unsupported"); + #endif + + static T cast(half arg) { return cast_impl(arg, is_float()); } + + private: + static T cast_impl(half arg, true_type) { return half2float(arg.data_); } + static T cast_impl(half arg, false_type) { return half2int(arg.data_); } + }; + template struct half_caster + { + #if HALF_ENABLE_CPP11_STATIC_ASSERT && HALF_ENABLE_CPP11_TYPE_TRAITS + static_assert(std::is_arithmetic::value, "half_cast to non-arithmetic type unsupported"); + #endif + + static T cast(expr arg) { return cast_impl(arg, is_float()); } + + private: + static T cast_impl(float arg, true_type) { return static_cast(arg); } + static T cast_impl(half arg, false_type) { return half2int(arg.data_); } + }; + template struct half_caster + { + static half cast(half arg) { return arg; } + }; + template struct half_caster : half_caster {}; + + /// \name Comparison operators + /// \{ + + /// Comparison for equality. + /// \param x first operand + /// \param y second operand + /// \retval true if operands equal + /// \retval false else + template typename enable::type operator==(T x, U y) { return functions::isequal(x, y); } + + /// Comparison for inequality. + /// \param x first operand + /// \param y second operand + /// \retval true if operands not equal + /// \retval false else + template typename enable::type operator!=(T x, U y) { return functions::isnotequal(x, y); } + + /// Comparison for less than. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x less than \a y + /// \retval false else + template typename enable::type operator<(T x, U y) { return functions::isless(x, y); } + + /// Comparison for greater than. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x greater than \a y + /// \retval false else + template typename enable::type operator>(T x, U y) { return functions::isgreater(x, y); } + + /// Comparison for less equal. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x less equal \a y + /// \retval false else + template typename enable::type operator<=(T x, U y) { return functions::islessequal(x, y); } + + /// Comparison for greater equal. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x greater equal \a y + /// \retval false else + template typename enable::type operator>=(T x, U y) { return functions::isgreaterequal(x, y); } + + /// \} + /// \name Arithmetic operators + /// \{ + + /// Add halfs. + /// \param x left operand + /// \param y right operand + /// \return sum of half expressions + template typename enable::type operator+(T x, U y) { return functions::plus(x, y); } + + /// Subtract halfs. + /// \param x left operand + /// \param y right operand + /// \return difference of half expressions + template typename enable::type operator-(T x, U y) { return functions::minus(x, y); } + + /// Multiply halfs. + /// \param x left operand + /// \param y right operand + /// \return product of half expressions + template typename enable::type operator*(T x, U y) { return functions::multiplies(x, y); } + + /// Divide halfs. + /// \param x left operand + /// \param y right operand + /// \return quotient of half expressions + template typename enable::type operator/(T x, U y) { return functions::divides(x, y); } + + /// Identity. + /// \param arg operand + /// \return uncahnged operand + template HALF_CONSTEXPR typename enable::type operator+(T arg) { return arg; } + + /// Negation. + /// \param arg operand + /// \return negated operand + template HALF_CONSTEXPR typename enable::type operator-(T arg) { return unary_specialized::negate(arg); } + + /// \} + /// \name Input and output + /// \{ + + /// Output operator. + /// \param out output stream to write into + /// \param arg half expression to write + /// \return reference to output stream + template typename enable&,T>::type + operator<<(std::basic_ostream &out, T arg) { return functions::write(out, arg); } + + /// Input operator. + /// \param in input stream to read from + /// \param arg half to read into + /// \return reference to input stream + template std::basic_istream& + operator>>(std::basic_istream &in, half &arg) { return functions::read(in, arg); } + + /// \} + /// \name Basic mathematical operations + /// \{ + + /// Absolute value. + /// \param arg operand + /// \return absolute value of \a arg +// template typename enable::type abs(T arg) { return unary_specialized::fabs(arg); } + inline half abs(half arg) { return unary_specialized::fabs(arg); } + inline expr abs(expr arg) { return unary_specialized::fabs(arg); } + + /// Absolute value. + /// \param arg operand + /// \return absolute value of \a arg +// template typename enable::type fabs(T arg) { return unary_specialized::fabs(arg); } + inline half fabs(half arg) { return unary_specialized::fabs(arg); } + inline expr fabs(expr arg) { return unary_specialized::fabs(arg); } + + /// Remainder of division. + /// \param x first operand + /// \param y second operand + /// \return remainder of floating point division. +// template typename enable::type fmod(T x, U y) { return functions::fmod(x, y); } + inline expr fmod(half x, half y) { return functions::fmod(x, y); } + inline expr fmod(half x, expr y) { return functions::fmod(x, y); } + inline expr fmod(expr x, half y) { return functions::fmod(x, y); } + inline expr fmod(expr x, expr y) { return functions::fmod(x, y); } + + /// Remainder of division. + /// \param x first operand + /// \param y second operand + /// \return remainder of floating point division. +// template typename enable::type remainder(T x, U y) { return functions::remainder(x, y); } + inline expr remainder(half x, half y) { return functions::remainder(x, y); } + inline expr remainder(half x, expr y) { return functions::remainder(x, y); } + inline expr remainder(expr x, half y) { return functions::remainder(x, y); } + inline expr remainder(expr x, expr y) { return functions::remainder(x, y); } + + /// Remainder of division. + /// \param x first operand + /// \param y second operand + /// \param quo address to store some bits of quotient at + /// \return remainder of floating point division. +// template typename enable::type remquo(T x, U y, int *quo) { return functions::remquo(x, y, quo); } + inline expr remquo(half x, half y, int *quo) { return functions::remquo(x, y, quo); } + inline expr remquo(half x, expr y, int *quo) { return functions::remquo(x, y, quo); } + inline expr remquo(expr x, half y, int *quo) { return functions::remquo(x, y, quo); } + inline expr remquo(expr x, expr y, int *quo) { return functions::remquo(x, y, quo); } + + /// Fused multiply add. + /// \param x first operand + /// \param y second operand + /// \param z third operand + /// \return ( \a x * \a y ) + \a z rounded as one operation. +// template typename enable::type fma(T x, U y, V z) { return functions::fma(x, y, z); } + inline expr fma(half x, half y, half z) { return functions::fma(x, y, z); } + inline expr fma(half x, half y, expr z) { return functions::fma(x, y, z); } + inline expr fma(half x, expr y, half z) { return functions::fma(x, y, z); } + inline expr fma(half x, expr y, expr z) { return functions::fma(x, y, z); } + inline expr fma(expr x, half y, half z) { return functions::fma(x, y, z); } + inline expr fma(expr x, half y, expr z) { return functions::fma(x, y, z); } + inline expr fma(expr x, expr y, half z) { return functions::fma(x, y, z); } + inline expr fma(expr x, expr y, expr z) { return functions::fma(x, y, z); } + + /// Maximum of half expressions. + /// \param x first operand + /// \param y second operand + /// \return maximum of operands +// template typename result::type fmax(T x, U y) { return binary_specialized::fmax(x, y); } + inline half fmax(half x, half y) { return binary_specialized::fmax(x, y); } + inline expr fmax(half x, expr y) { return binary_specialized::fmax(x, y); } + inline expr fmax(expr x, half y) { return binary_specialized::fmax(x, y); } + inline expr fmax(expr x, expr y) { return binary_specialized::fmax(x, y); } + + /// Minimum of half expressions. + /// \param x first operand + /// \param y second operand + /// \return minimum of operands +// template typename result::type fmin(T x, U y) { return binary_specialized::fmin(x, y); } + inline half fmin(half x, half y) { return binary_specialized::fmin(x, y); } + inline expr fmin(half x, expr y) { return binary_specialized::fmin(x, y); } + inline expr fmin(expr x, half y) { return binary_specialized::fmin(x, y); } + inline expr fmin(expr x, expr y) { return binary_specialized::fmin(x, y); } + + /// Positive difference. + /// \param x first operand + /// \param y second operand + /// \return \a x - \a y or 0 if difference negative +// template typename enable::type fdim(T x, U y) { return functions::fdim(x, y); } + inline expr fdim(half x, half y) { return functions::fdim(x, y); } + inline expr fdim(half x, expr y) { return functions::fdim(x, y); } + inline expr fdim(expr x, half y) { return functions::fdim(x, y); } + inline expr fdim(expr x, expr y) { return functions::fdim(x, y); } + + /// Get NaN value. + /// \return quiet NaN + inline half nanh(const char*) { return functions::nanh(); } + + /// \} + /// \name Exponential functions + /// \{ + + /// Exponential function. + /// \param arg function argument + /// \return e raised to \a arg +// template typename enable::type exp(T arg) { return functions::exp(arg); } + inline expr exp(half arg) { return functions::exp(arg); } + inline expr exp(expr arg) { return functions::exp(arg); } + + /// Exponential minus one. + /// \param arg function argument + /// \return e raised to \a arg subtracted by 1 +// template typename enable::type expm1(T arg) { return functions::expm1(arg); } + inline expr expm1(half arg) { return functions::expm1(arg); } + inline expr expm1(expr arg) { return functions::expm1(arg); } + + /// Binary exponential. + /// \param arg function argument + /// \return 2 raised to \a arg +// template typename enable::type exp2(T arg) { return functions::exp2(arg); } + inline expr exp2(half arg) { return functions::exp2(arg); } + inline expr exp2(expr arg) { return functions::exp2(arg); } + + /// Natural logorithm. + /// \param arg function argument + /// \return logarithm of \a arg to base e +// template typename enable::type log(T arg) { return functions::log(arg); } + inline expr log(half arg) { return functions::log(arg); } + inline expr log(expr arg) { return functions::log(arg); } + + /// Common logorithm. + /// \param arg function argument + /// \return logarithm of \a arg to base 10 +// template typename enable::type log10(T arg) { return functions::log10(arg); } + inline expr log10(half arg) { return functions::log10(arg); } + inline expr log10(expr arg) { return functions::log10(arg); } + + /// Natural logorithm. + /// \param arg function argument + /// \return logarithm of \a arg plus 1 to base e +// template typename enable::type log1p(T arg) { return functions::log1p(arg); } + inline expr log1p(half arg) { return functions::log1p(arg); } + inline expr log1p(expr arg) { return functions::log1p(arg); } + + /// Binary logorithm. + /// \param arg function argument + /// \return logarithm of \a arg to base 2 +// template typename enable::type log2(T arg) { return functions::log2(arg); } + inline expr log2(half arg) { return functions::log2(arg); } + inline expr log2(expr arg) { return functions::log2(arg); } + + /// \} + /// \name Power functions + /// \{ + + /// Square root. + /// \param arg function argument + /// \return square root of \a arg +// template typename enable::type sqrt(T arg) { return functions::sqrt(arg); } + inline expr sqrt(half arg) { return functions::sqrt(arg); } + inline expr sqrt(expr arg) { return functions::sqrt(arg); } + + /// Cubic root. + /// \param arg function argument + /// \return cubic root of \a arg +// template typename enable::type cbrt(T arg) { return functions::cbrt(arg); } + inline expr cbrt(half arg) { return functions::cbrt(arg); } + inline expr cbrt(expr arg) { return functions::cbrt(arg); } + + /// Hypotenuse function. + /// \param x first argument + /// \param y second argument + /// \return square root of sum of squares without internal over- or underflows +// template typename enable::type hypot(T x, U y) { return functions::hypot(x, y); } + inline expr hypot(half x, half y) { return functions::hypot(x, y); } + inline expr hypot(half x, expr y) { return functions::hypot(x, y); } + inline expr hypot(expr x, half y) { return functions::hypot(x, y); } + inline expr hypot(expr x, expr y) { return functions::hypot(x, y); } + + /// Power function. + /// \param base first argument + /// \param exp second argument + /// \return \a base raised to \a exp +// template typename enable::type pow(T base, U exp) { return functions::pow(base, exp); } + inline expr pow(half base, half exp) { return functions::pow(base, exp); } + inline expr pow(half base, expr exp) { return functions::pow(base, exp); } + inline expr pow(expr base, half exp) { return functions::pow(base, exp); } + inline expr pow(expr base, expr exp) { return functions::pow(base, exp); } + + /// \} + /// \name Trigonometric functions + /// \{ + + /// Sine function. + /// \param arg function argument + /// \return sine value of \a arg +// template typename enable::type sin(T arg) { return functions::sin(arg); } + inline expr sin(half arg) { return functions::sin(arg); } + inline expr sin(expr arg) { return functions::sin(arg); } + + /// Cosine function. + /// \param arg function argument + /// \return cosine value of \a arg +// template typename enable::type cos(T arg) { return functions::cos(arg); } + inline expr cos(half arg) { return functions::cos(arg); } + inline expr cos(expr arg) { return functions::cos(arg); } + + /// Tangent function. + /// \param arg function argument + /// \return tangent value of \a arg +// template typename enable::type tan(T arg) { return functions::tan(arg); } + inline expr tan(half arg) { return functions::tan(arg); } + inline expr tan(expr arg) { return functions::tan(arg); } + + /// Arc sine. + /// \param arg function argument + /// \return arc sine value of \a arg +// template typename enable::type asin(T arg) { return functions::asin(arg); } + inline expr asin(half arg) { return functions::asin(arg); } + inline expr asin(expr arg) { return functions::asin(arg); } + + /// Arc cosine function. + /// \param arg function argument + /// \return arc cosine value of \a arg +// template typename enable::type acos(T arg) { return functions::acos(arg); } + inline expr acos(half arg) { return functions::acos(arg); } + inline expr acos(expr arg) { return functions::acos(arg); } + + /// Arc tangent function. + /// \param arg function argument + /// \return arc tangent value of \a arg +// template typename enable::type atan(T arg) { return functions::atan(arg); } + inline expr atan(half arg) { return functions::atan(arg); } + inline expr atan(expr arg) { return functions::atan(arg); } + + /// Arc tangent function. + /// \param x first argument + /// \param y second argument + /// \return arc tangent value +// template typename enable::type atan2(T x, U y) { return functions::atan2(x, y); } + inline expr atan2(half x, half y) { return functions::atan2(x, y); } + inline expr atan2(half x, expr y) { return functions::atan2(x, y); } + inline expr atan2(expr x, half y) { return functions::atan2(x, y); } + inline expr atan2(expr x, expr y) { return functions::atan2(x, y); } + + /// \} + /// \name Hyperbolic functions + /// \{ + + /// Hyperbolic sine. + /// \param arg function argument + /// \return hyperbolic sine value of \a arg +// template typename enable::type sinh(T arg) { return functions::sinh(arg); } + inline expr sinh(half arg) { return functions::sinh(arg); } + inline expr sinh(expr arg) { return functions::sinh(arg); } + + /// Hyperbolic cosine. + /// \param arg function argument + /// \return hyperbolic cosine value of \a arg +// template typename enable::type cosh(T arg) { return functions::cosh(arg); } + inline expr cosh(half arg) { return functions::cosh(arg); } + inline expr cosh(expr arg) { return functions::cosh(arg); } + + /// Hyperbolic tangent. + /// \param arg function argument + /// \return hyperbolic tangent value of \a arg +// template typename enable::type tanh(T arg) { return functions::tanh(arg); } + inline expr tanh(half arg) { return functions::tanh(arg); } + inline expr tanh(expr arg) { return functions::tanh(arg); } + + /// Hyperbolic area sine. + /// \param arg function argument + /// \return area sine value of \a arg +// template typename enable::type asinh(T arg) { return functions::asinh(arg); } + inline expr asinh(half arg) { return functions::asinh(arg); } + inline expr asinh(expr arg) { return functions::asinh(arg); } + + /// Hyperbolic area cosine. + /// \param arg function argument + /// \return area cosine value of \a arg +// template typename enable::type acosh(T arg) { return functions::acosh(arg); } + inline expr acosh(half arg) { return functions::acosh(arg); } + inline expr acosh(expr arg) { return functions::acosh(arg); } + + /// Hyperbolic area tangent. + /// \param arg function argument + /// \return area tangent value of \a arg +// template typename enable::type atanh(T arg) { return functions::atanh(arg); } + inline expr atanh(half arg) { return functions::atanh(arg); } + inline expr atanh(expr arg) { return functions::atanh(arg); } + + /// \} + /// \name Error and gamma functions + /// \{ + + /// Error function. + /// \param arg function argument + /// \return error function value of \a arg +// template typename enable::type erf(T arg) { return functions::erf(arg); } + inline expr erf(half arg) { return functions::erf(arg); } + inline expr erf(expr arg) { return functions::erf(arg); } + + /// Complementary error function. + /// \param arg function argument + /// \return 1 minus error function value of \a arg +// template typename enable::type erfc(T arg) { return functions::erfc(arg); } + inline expr erfc(half arg) { return functions::erfc(arg); } + inline expr erfc(expr arg) { return functions::erfc(arg); } + + /// Natural logarithm of gamma function. + /// \param arg function argument + /// \return natural logarith of gamma function for \a arg +// template typename enable::type lgamma(T arg) { return functions::lgamma(arg); } + inline expr lgamma(half arg) { return functions::lgamma(arg); } + inline expr lgamma(expr arg) { return functions::lgamma(arg); } + + /// Gamma function. + /// \param arg function argument + /// \return gamma function value of \a arg +// template typename enable::type tgamma(T arg) { return functions::tgamma(arg); } + inline expr tgamma(half arg) { return functions::tgamma(arg); } + inline expr tgamma(expr arg) { return functions::tgamma(arg); } + + /// \} + /// \name Rounding + /// \{ + + /// Nearest integer not less than half value. + /// \param arg half to round + /// \return nearest integer not less than \a arg +// template typename enable::type ceil(T arg) { return functions::ceil(arg); } + inline half ceil(half arg) { return functions::ceil(arg); } + inline half ceil(expr arg) { return functions::ceil(arg); } + + /// Nearest integer not greater than half value. + /// \param arg half to round + /// \return nearest integer not greater than \a arg +// template typename enable::type floor(T arg) { return functions::floor(arg); } + inline half floor(half arg) { return functions::floor(arg); } + inline half floor(expr arg) { return functions::floor(arg); } + + /// Nearest integer not greater in magnitude than half value. + /// \param arg half to round + /// \return nearest integer not greater in magnitude than \a arg +// template typename enable::type trunc(T arg) { return functions::trunc(arg); } + inline half trunc(half arg) { return functions::trunc(arg); } + inline half trunc(expr arg) { return functions::trunc(arg); } + + /// Nearest integer. + /// \param arg half to round + /// \return nearest integer, rounded away from zero in half-way cases +// template typename enable::type round(T arg) { return functions::round(arg); } + inline half round(half arg) { return functions::round(arg); } + inline half round(expr arg) { return functions::round(arg); } + + /// Nearest integer. + /// \param arg half to round + /// \return nearest integer, rounded away from zero in half-way cases +// template typename enable::type lround(T arg) { return functions::lround(arg); } + inline long lround(half arg) { return functions::lround(arg); } + inline long lround(expr arg) { return functions::lround(arg); } + + /// Nearest integer using half's internal rounding mode. + /// \param arg half expression to round + /// \return nearest integer using default rounding mode +// template typename enable::type nearbyint(T arg) { return functions::nearbyint(arg); } + inline half nearbyint(half arg) { return functions::rint(arg); } + inline half nearbyint(expr arg) { return functions::rint(arg); } + + /// Nearest integer using half's internal rounding mode. + /// \param arg half expression to round + /// \return nearest integer using default rounding mode +// template typename enable::type rint(T arg) { return functions::rint(arg); } + inline half rint(half arg) { return functions::rint(arg); } + inline half rint(expr arg) { return functions::rint(arg); } + + /// Nearest integer using half's internal rounding mode. + /// \param arg half expression to round + /// \return nearest integer using default rounding mode +// template typename enable::type lrint(T arg) { return functions::lrint(arg); } + inline long lrint(half arg) { return functions::lrint(arg); } + inline long lrint(expr arg) { return functions::lrint(arg); } + #if HALF_ENABLE_CPP11_LONG_LONG + /// Nearest integer. + /// \param arg half to round + /// \return nearest integer, rounded away from zero in half-way cases +// template typename enable::type llround(T arg) { return functions::llround(arg); } + inline long long llround(half arg) { return functions::llround(arg); } + inline long long llround(expr arg) { return functions::llround(arg); } + + /// Nearest integer using half's internal rounding mode. + /// \param arg half expression to round + /// \return nearest integer using default rounding mode +// template typename enable::type llrint(T arg) { return functions::llrint(arg); } + inline long long llrint(half arg) { return functions::llrint(arg); } + inline long long llrint(expr arg) { return functions::llrint(arg); } + #endif + + /// \} + /// \name Floating point manipulation + /// \{ + + /// Decompress floating point number. + /// \param arg number to decompress + /// \param exp address to store exponent at + /// \return significant in range [0.5, 1) +// template typename enable::type frexp(T arg, int *exp) { return functions::frexp(arg, exp); } + inline half frexp(half arg, int *exp) { return functions::frexp(arg, exp); } + inline half frexp(expr arg, int *exp) { return functions::frexp(arg, exp); } + + /// Multiply by power of two. + /// \param arg number to modify + /// \param exp power of two to multiply with + /// \return \a arg multplied by 2 raised to \a exp +// template typename enable::type ldexp(T arg, int exp) { return functions::scalbln(arg, exp); } + inline half ldexp(half arg, int exp) { return functions::scalbln(arg, exp); } + inline half ldexp(expr arg, int exp) { return functions::scalbln(arg, exp); } + + /// Extract integer and fractional parts. + /// \param arg number to decompress + /// \param iptr address to store integer part at + /// \return fractional part +// template typename enable::type modf(T arg, half *iptr) { return functions::modf(arg, iptr); } + inline half modf(half arg, half *iptr) { return functions::modf(arg, iptr); } + inline half modf(expr arg, half *iptr) { return functions::modf(arg, iptr); } + + /// Multiply by power of two. + /// \param arg number to modify + /// \param exp power of two to multiply with + /// \return \a arg multplied by 2 raised to \a exp +// template typename enable::type scalbn(T arg, int exp) { return functions::scalbln(arg, exp); } + inline half scalbn(half arg, int exp) { return functions::scalbln(arg, exp); } + inline half scalbn(expr arg, int exp) { return functions::scalbln(arg, exp); } + + /// Multiply by power of two. + /// \param arg number to modify + /// \param exp power of two to multiply with + /// \return \a arg multplied by 2 raised to \a exp +// template typename enable::type scalbln(T arg, long exp) { return functions::scalbln(arg, exp); } + inline half scalbln(half arg, long exp) { return functions::scalbln(arg, exp); } + inline half scalbln(expr arg, long exp) { return functions::scalbln(arg, exp); } + + /// Extract exponent. + /// \param arg number to query + /// \return floating point exponent + /// \retval FP_ILOGB0 for zero + /// \retval FP_ILOGBNAN for NaN + /// \retval MAX_INT for infinity +// template typename enable::type ilogb(T arg) { return functions::ilogb(arg); } + inline int ilogb(half arg) { return functions::ilogb(arg); } + inline int ilogb(expr arg) { return functions::ilogb(arg); } + + /// Extract exponent. + /// \param arg number to query + /// \return floating point exponent +// template typename enable::type logb(T arg) { return functions::logb(arg); } + inline half logb(half arg) { return functions::logb(arg); } + inline half logb(expr arg) { return functions::logb(arg); } + + /// Next representable value. + /// \param from value to compute next representable value for + /// \param to direction towards which to compute next value + /// \return next representable value after \a from in direction towards \a to +// template typename enable::type nextafter(T from, U to) { return functions::nextafter(from, to); } + inline half nextafter(half from, half to) { return functions::nextafter(from, to); } + inline half nextafter(half from, expr to) { return functions::nextafter(from, to); } + inline half nextafter(expr from, half to) { return functions::nextafter(from, to); } + inline half nextafter(expr from, expr to) { return functions::nextafter(from, to); } + + /// Next representable value. + /// \param from value to compute next representable value for + /// \param to direction towards which to compute next value + /// \return next representable value after \a from in direction towards \a to +// template typename enable::type nexttoward(T from, long double to) { return functions::nexttoward(from, to); } + inline half nexttoward(half from, long double to) { return functions::nexttoward(from, to); } + inline half nexttoward(expr from, long double to) { return functions::nexttoward(from, to); } + + /// Take sign. + /// \param x value to change sign for + /// \param y value to take sign from + /// \return value equal to \a x in magnitude and to \a y in sign +// template typename enable::type copysign(T x, U y) { return functions::copysign(x, y); } + inline half copysign(half x, half y) { return functions::copysign(x, y); } + inline half copysign(half x, expr y) { return functions::copysign(x, y); } + inline half copysign(expr x, half y) { return functions::copysign(x, y); } + inline half copysign(expr x, expr y) { return functions::copysign(x, y); } + + /// \} + /// \name Floating point classification + /// \{ + + + /// Classify floating point value. + /// \param arg number to classify + /// \retval FP_ZERO for positive and negative zero + /// \retval FP_SUBNORMAL for subnormal numbers + /// \retval FP_INFINITY for positive and negative infinity + /// \retval FP_NAN for NaNs + /// \retval FP_NORMAL for all other (normal) values +// template typename enable::type fpclassify(T arg) { return functions::fpclassify(arg); } + inline int fpclassify(half arg) { return functions::fpclassify(arg); } + inline int fpclassify(expr arg) { return functions::fpclassify(arg); } + + /// Check if finite number. + /// \param arg number to check + /// \retval true if neither infinity nor NaN + /// \retval false else +// template typename enable::type isfinite(T arg) { return functions::isfinite(arg); } + inline bool isfinite(half arg) { return functions::isfinite(arg); } + inline bool isfinite(expr arg) { return functions::isfinite(arg); } + + /// Check for infinity. + /// \param arg number to check + /// \retval true for positive or negative infinity + /// \retval false else +// template typename enable::type isinf(T arg) { return functions::isinf(arg); } + inline bool isinf(half arg) { return functions::isinf(arg); } + inline bool isinf(expr arg) { return functions::isinf(arg); } + + /// Check for NaN. + /// \param arg number to check + /// \retval true for NaNs + /// \retval false else +// template typename enable::type isnan(T arg) { return functions::isnan(arg); } + inline bool isnan(half arg) { return functions::isnan(arg); } + inline bool isnan(expr arg) { return functions::isnan(arg); } + + /// Check if normal number. + /// \param arg number to check + /// \retval true if normal number + /// \retval false if either subnormal, zero, infinity or NaN +// template typename enable::type isnormal(T arg) { return functions::isnormal(arg); } + inline bool isnormal(half arg) { return functions::isnormal(arg); } + inline bool isnormal(expr arg) { return functions::isnormal(arg); } + + /// Check sign. + /// \param arg number to check + /// \retval true for negative number + /// \retval false for positive number +// template typename enable::type signbit(T arg) { return functions::signbit(arg); } + inline bool signbit(half arg) { return functions::signbit(arg); } + inline bool signbit(expr arg) { return functions::signbit(arg); } + + /// \} + /// \name Comparison + /// \{ + + /// Comparison for greater than. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x greater than \a y + /// \retval false else +// template typename enable::type isgreater(T x, U y) { return functions::isgreater(x, y); } + inline bool isgreater(half x, half y) { return functions::isgreater(x, y); } + inline bool isgreater(half x, expr y) { return functions::isgreater(x, y); } + inline bool isgreater(expr x, half y) { return functions::isgreater(x, y); } + inline bool isgreater(expr x, expr y) { return functions::isgreater(x, y); } + + /// Comparison for greater equal. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x greater equal \a y + /// \retval false else +// template typename enable::type isgreaterequal(T x, U y) { return functions::isgreaterequal(x, y); } + inline bool isgreaterequal(half x, half y) { return functions::isgreaterequal(x, y); } + inline bool isgreaterequal(half x, expr y) { return functions::isgreaterequal(x, y); } + inline bool isgreaterequal(expr x, half y) { return functions::isgreaterequal(x, y); } + inline bool isgreaterequal(expr x, expr y) { return functions::isgreaterequal(x, y); } + + /// Comparison for less than. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x less than \a y + /// \retval false else +// template typename enable::type isless(T x, U y) { return functions::isless(x, y); } + inline bool isless(half x, half y) { return functions::isless(x, y); } + inline bool isless(half x, expr y) { return functions::isless(x, y); } + inline bool isless(expr x, half y) { return functions::isless(x, y); } + inline bool isless(expr x, expr y) { return functions::isless(x, y); } + + /// Comparison for less equal. + /// \param x first operand + /// \param y second operand + /// \retval true if \a x less equal \a y + /// \retval false else +// template typename enable::type islessequal(T x, U y) { return functions::islessequal(x, y); } + inline bool islessequal(half x, half y) { return functions::islessequal(x, y); } + inline bool islessequal(half x, expr y) { return functions::islessequal(x, y); } + inline bool islessequal(expr x, half y) { return functions::islessequal(x, y); } + inline bool islessequal(expr x, expr y) { return functions::islessequal(x, y); } + + /// Comarison for less or greater. + /// \param x first operand + /// \param y second operand + /// \retval true if either less or greater + /// \retval false else +// template typename enable::type islessgreater(T x, U y) { return functions::islessgreater(x, y); } + inline bool islessgreater(half x, half y) { return functions::islessgreater(x, y); } + inline bool islessgreater(half x, expr y) { return functions::islessgreater(x, y); } + inline bool islessgreater(expr x, half y) { return functions::islessgreater(x, y); } + inline bool islessgreater(expr x, expr y) { return functions::islessgreater(x, y); } + + /// Check if unordered. + /// \param x first operand + /// \param y second operand + /// \retval true if unordered (one or two NaN operands) + /// \retval false else +// template typename enable::type isunordered(T x, U y) { return functions::isunordered(x, y); } + inline bool isunordered(half x, half y) { return functions::isunordered(x, y); } + inline bool isunordered(half x, expr y) { return functions::isunordered(x, y); } + inline bool isunordered(expr x, half y) { return functions::isunordered(x, y); } + inline bool isunordered(expr x, expr y) { return functions::isunordered(x, y); } + + /// \name Casting + /// \{ + + /// Cast to or from half-precision floating point number. + /// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values are converted + /// directly using the given rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do. + /// It uses the default rounding mode. + /// + /// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types + /// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler + /// error and casting between [half](\ref half_float::half)s is just a no-op. + /// \tparam T destination type (half or built-in arithmetic type) + /// \tparam U source type (half or built-in arithmetic type) + /// \param arg value to cast + /// \return \a arg converted to destination type + template T half_cast(U arg) { return half_caster::cast(arg); } + + /// Cast to or from half-precision floating point number. + /// This casts between [half](\ref half_float::half) and any built-in arithmetic type. The values are converted + /// directly using the given rounding mode, without any roundtrip over `float` that a `static_cast` would otherwise do. + /// + /// Using this cast with neither of the two types being a [half](\ref half_float::half) or with any of the two types + /// not being a built-in arithmetic type (apart from [half](\ref half_float::half), of course) results in a compiler + /// error and casting between [half](\ref half_float::half)s is just a no-op. + /// \tparam T destination type (half or built-in arithmetic type) + /// \tparam R rounding mode to use. + /// \tparam U source type (half or built-in arithmetic type) + /// \param arg value to cast + /// \return \a arg converted to destination type + template T half_cast(U arg) { return half_caster::cast(arg); } + /// \} + } + + using detail::operator==; + using detail::operator!=; + using detail::operator<; + using detail::operator>; + using detail::operator<=; + using detail::operator>=; + using detail::operator+; + using detail::operator-; + using detail::operator*; + using detail::operator/; + using detail::operator<<; + using detail::operator>>; + + using detail::abs; + using detail::fabs; + using detail::fmod; + using detail::remainder; + using detail::remquo; + using detail::fma; + using detail::fmax; + using detail::fmin; + using detail::fdim; + using detail::nanh; + using detail::exp; + using detail::expm1; + using detail::exp2; + using detail::log; + using detail::log10; + using detail::log1p; + using detail::log2; + using detail::sqrt; + using detail::cbrt; + using detail::hypot; + using detail::pow; + using detail::sin; + using detail::cos; + using detail::tan; + using detail::asin; + using detail::acos; + using detail::atan; + using detail::atan2; + using detail::sinh; + using detail::cosh; + using detail::tanh; + using detail::asinh; + using detail::acosh; + using detail::atanh; + using detail::erf; + using detail::erfc; + using detail::lgamma; + using detail::tgamma; + using detail::ceil; + using detail::floor; + using detail::trunc; + using detail::round; + using detail::lround; + using detail::nearbyint; + using detail::rint; + using detail::lrint; +#if HALF_ENABLE_CPP11_LONG_LONG + using detail::llround; + using detail::llrint; +#endif + using detail::frexp; + using detail::ldexp; + using detail::modf; + using detail::scalbn; + using detail::scalbln; + using detail::ilogb; + using detail::logb; + using detail::nextafter; + using detail::nexttoward; + using detail::copysign; + using detail::fpclassify; + using detail::isfinite; + using detail::isinf; + using detail::isnan; + using detail::isnormal; + using detail::signbit; + using detail::isgreater; + using detail::isgreaterequal; + using detail::isless; + using detail::islessequal; + using detail::islessgreater; + using detail::isunordered; + + using detail::half_cast; +} + + +/// Extensions to the C++ standard library. +namespace std +{ + /// Numeric limits for half-precision floats. + /// Because of the underlying single-precision implementation of many operations, it inherits some properties from + /// `std::numeric_limits`. + template<> class numeric_limits : public numeric_limits + { + public: + /// Supports signed values. + static HALF_CONSTEXPR_CONST bool is_signed = true; + + /// Is not exact. + static HALF_CONSTEXPR_CONST bool is_exact = false; + + /// Doesn't provide modulo arithmetic. + static HALF_CONSTEXPR_CONST bool is_modulo = false; + + /// IEEE conformant. + static HALF_CONSTEXPR_CONST bool is_iec559 = true; + + /// Supports infinity. + static HALF_CONSTEXPR_CONST bool has_infinity = true; + + /// Supports quiet NaNs. + static HALF_CONSTEXPR_CONST bool has_quiet_NaN = true; + + /// Supports subnormal values. + static HALF_CONSTEXPR_CONST float_denorm_style has_denorm = denorm_present; + + /// Rounding mode. + /// Due to the mix of internal single-precision computations (using the rounding mode of the underlying + /// single-precision implementation) with the rounding mode of the single-to-half conversions, the actual rounding + /// mode might be `std::round_indeterminate` if the default half-precision rounding mode doesn't match the + /// single-precision rounding mode. + static HALF_CONSTEXPR_CONST float_round_style round_style = (std::numeric_limits::round_style== + half_float::half::round_style) ? half_float::half::round_style : round_indeterminate; + + /// Significant digits. + static HALF_CONSTEXPR_CONST int digits = 11; + + /// Significant decimal digits. + static HALF_CONSTEXPR_CONST int digits10 = 3; + + /// Required decimal digits to represent all possible values. + static HALF_CONSTEXPR_CONST int max_digits10 = 5; + + /// Number base. + static HALF_CONSTEXPR_CONST int radix = 2; + + /// One more than smallest exponent. + static HALF_CONSTEXPR_CONST int min_exponent = -13; + + /// Smallest normalized representable power of 10. + static HALF_CONSTEXPR_CONST int min_exponent10 = -4; + + /// One more than largest exponent + static HALF_CONSTEXPR_CONST int max_exponent = 16; + + /// Largest finitely representable power of 10. + static HALF_CONSTEXPR_CONST int max_exponent10 = 4; + + /// Smallest positive normal value. + static HALF_CONSTEXPR half_float::half min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0400); } + + /// Smallest finite value. + static HALF_CONSTEXPR half_float::half lowest() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0xFBFF); } + + /// Largest finite value. + static HALF_CONSTEXPR half_float::half max() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7BFF); } + + /// Difference between one and next representable value. + static HALF_CONSTEXPR half_float::half epsilon() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x1400); } + + /// Maximum rounding error. + static HALF_CONSTEXPR half_float::half round_error() HALF_NOTHROW + { return half_float::half(half_float::detail::binary, (round_style==std::round_to_nearest) ? 0x3800 : 0x3C00); } + + /// Positive infinity. + static HALF_CONSTEXPR half_float::half infinity() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7C00); } + + /// Quiet NaN. + static HALF_CONSTEXPR half_float::half quiet_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7FFF); } + + /// Signalling NaN. + static HALF_CONSTEXPR half_float::half signaling_NaN() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x7DFF); } + + /// Smallest positive subnormal value. + static HALF_CONSTEXPR half_float::half denorm_min() HALF_NOTHROW { return half_float::half(half_float::detail::binary, 0x0001); } + }; + +#if HALF_ENABLE_CPP11_HASH + /// Hash function for half-precision floats. + /// This is only defined if C++11 `std::hash` is supported and enabled. + template<> struct hash //: unary_function + { + /// Type of function argument. + typedef half_float::half argument_type; + + /// Function return type. + typedef size_t result_type; + + /// Compute hash function. + /// \param arg half to hash + /// \return hash value + result_type operator()(argument_type arg) const + { return hash()(static_cast(arg.data_)&-(arg.data_!=0x8000)); } + }; +#endif +} + + +#undef HALF_CONSTEXPR +#undef HALF_CONSTEXPR_CONST +#undef HALF_NOEXCEPT +#undef HALF_NOTHROW +#ifdef HALF_POP_WARNINGS + #pragma warning(pop) + #undef HALF_POP_WARNINGS +#endif + +#endif